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Ayan Mukhopadhyay

Ayan Mukhopadhyay appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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hep-thgr-qcArtificial Intelligencehep-phnucl-thMachine Learningcond-mat.str-elcs.CYeess.SYMultiagent Systemsquant-phSystems and Controlcond-mat.stat-mecheess.SPHuman-Computer Interactionmath-phmath.MPmath.OC

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Published work

32 published item(s)

preprint2026arXiv

Grid-Aware Charging and Operational Optimization for Mixed-Fleet Public Transit

The rapid growth of urban populations and the increasing need for sustainable transportation solutions have prompted a shift towards electric buses in public transit systems. However, the effective management of mixed fleets consisting of both electric and diesel buses poses significant operational challenges. One major challenge is coping with dynamic electricity pricing, where charging costs vary throughout the day. Transit agencies must optimize charging assignments in response to such dynamism while accounting for secondary considerations such as seating constraints. This paper presents a comprehensive mixed-integer linear programming (MILP) model to address these challenges by jointly optimizing charging schedules and trip assignments for mixed (electric and diesel bus) fleets while considering factors such as dynamic electricity pricing, vehicle capacity, and route constraints. We address the potential computational intractability of the MILP formulation, which can arise even with relatively small fleets, by employing a hierarchical approach tailored to the fleet composition. By using real-world data from the city of Chattanooga, Tennessee, USA, we show that our approach can result in significant savings in the operating costs of the mixed transit fleets.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Hybrid thermalization in the large $N$ limit

Semi-holography provides a formulation of dynamics in gauge theories involving both weakly self-interacting (perturbative) and strongly self-interacting (non-perturbative) degrees of freedom. These two subsectors interact via their effective metrics and sources, while the full local energy-momentum tensor is conserved in the physical background metric. In the large $N$ limit, the subsectors have their individual entropy currents, and so the full system can reach a pseudo-equilibrium state in which each subsector has a different physical temperature. We first complete the proof that the global thermal equilibrium state, where both subsectors have the \textit{same} physical temperature, can be defined in consistency with the principles of thermodynamics and statistical mechanics. Particularly, we show that the global equilibrium state is the unique state with maximum entropy in the microcanonical ensemble. Furthermore, we show that in the large $N$ limit, a \textit{typical} non-equilibrium state of the full isolated system relaxes to the global equilibrium state when the average energy density is large compared to the scale set by the inter-system coupling. We discuss quantum statistical perspectives.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Online Decision-Making Under Uncertainty for Vehicle-to-Building Systems

Vehicle-to-building (V2B) systems integrate physical infrastructures, such as smart buildings and electric vehicles (EVs) connected to chargers at the building, with digital control mechanisms to manage energy use. By utilizing EVs as flexible energy reservoirs, buildings can dynamically charge and discharge them to optimize energy use and cut costs under time-variable pricing and demand charge policies. This setup leads to the V2B optimization problem, where buildings coordinate EV charging and discharging to minimize total electricity costs while meeting users' charging requirements. However, the V2B optimization problem is challenging because of: (1) fluctuating electricity pricing, which includes both energy charges ($/kWh) and demand charges ($/kW); (2) long planning horizons (typically over 30 days); (3) heterogeneous chargers with varying charging rates, controllability, and directionality (i.e., unidirectional or bidirectional); and (4) user-specific battery levels at departure to ensure user requirements are met. In contrast to existing approaches that often model this setting as a single-shot combinatorial optimization problem, we highlight critical limitations in prior work and instead model the V2B optimization problem as a Markov decision process (MDP), i.e., a stochastic control process. Solving the resulting MDP is challenging due to the large state and action spaces. To address the challenges of the large state space, we leverage online search, and we counter the action space by using domain-specific heuristics to prune unpromising actions. We validate our approach in collaboration with Nissan Advanced Technology Center - Silicon Valley. Using data from their EV testbed, we show that the proposed framework significantly outperforms state-of-the-art methods.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Toward Template-Free Explainability for Monte Carlo Tree Search

Probabilistic search algorithms, such as Monte Carlo Tree Search (MCTS), have proven very effective in solving sequential decision-making tasks under uncertainty. However, interpreting asymmetric search trees that incorporate bandit-based tree traversal and simulation-based value estimation is difficult for end users based solely on raw tree statistics. While prior work requires hand-crafted formal logic constraints that must be updated when the problem changes, we present a framework that enables large language models (LLMs) to generate evidence-grounded explanations of MCTS decisions from recorded search traces in an end-to-end manner. Our framework maps natural-language questions to a structured set of intent categories, determines whether the existing tree contains sufficient evidence, triggers targeted expansion when needed, and generates explanations using tree statistics such as visit counts, value estimates, and risk information. Experimental results provide the first evidence that LLMs can serve as end-to-end explainers for probabilistic search, without requiring intermediate formal representations.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

ADVISER: AI-Driven Vaccination Intervention Optimiser for Increasing Vaccine Uptake in Nigeria

More than 5 million children under five years die from largely preventable or treatable medical conditions every year, with an overwhelmingly large proportion of deaths occurring in under-developed countries with low vaccination uptake. One of the United Nations' sustainable development goals (SDG 3) aims to end preventable deaths of newborns and children under five years of age. We focus on Nigeria, where the rate of infant mortality is appalling. We collaborate with HelpMum, a large non-profit organization in Nigeria to design and optimize the allocation of heterogeneous health interventions under uncertainty to increase vaccination uptake, the first such collaboration in Nigeria. Our framework, ADVISER: AI-Driven Vaccination Intervention Optimiser, is based on an integer linear program that seeks to maximize the cumulative probability of successful vaccination. Our optimization formulation is intractable in practice. We present a heuristic approach that enables us to solve the problem for real-world use-cases. We also present theoretical bounds for the heuristic method. Finally, we show that the proposed approach outperforms baseline methods in terms of vaccination uptake through experimental evaluation. HelpMum is currently planning a pilot program based on our approach to be deployed in the largest city of Nigeria, which would be the first deployment of an AI-driven vaccination uptake program in the country and hopefully, pave the way for other data-driven programs to improve health outcomes in Nigeria.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

An Online Approach to Solve the Dynamic Vehicle Routing Problem with Stochastic Trip Requests for Paratransit Services

Many transit agencies operating paratransit and microtransit services have to respond to trip requests that arrive in real-time, which entails solving hard combinatorial and sequential decision-making problems under uncertainty. To avoid decisions that lead to significant inefficiency in the long term, vehicles should be allocated to requests by optimizing a non-myopic utility function or by batching requests together and optimizing a myopic utility function. While the former approach is typically offline, the latter can be performed online. We point out two major issues with such approaches when applied to paratransit services in practice. First, it is difficult to batch paratransit requests together as they are temporally sparse. Second, the environment in which transit agencies operate changes dynamically (e.g., traffic conditions), causing estimates that are learned offline to become stale. To address these challenges, we propose a fully online approach to solve the dynamic vehicle routing problem (DVRP) with time windows and stochastic trip requests that is robust to changing environmental dynamics by construction. We focus on scenarios where requests are relatively sparse - our problem is motivated by applications to paratransit services. We formulate DVRP as a Markov decision process and use Monte Carlo tree search to evaluate actions for any given state. Accounting for stochastic requests while optimizing a non-myopic utility function is computationally challenging; indeed, the action space for such a problem is intractably large in practice. To tackle the large action space, we leverage the structure of the problem to design heuristics that can sample promising actions for the tree search. Our experiments using real-world data from our partner agency show that the proposed approach outperforms existing state-of-the-art approaches both in terms of performance and robustness.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Decision Making in Non-Stationary Environments with Policy-Augmented Monte Carlo Tree Search

Decision-making under uncertainty (DMU) is present in many important problems. An open challenge is DMU in non-stationary environments, where the dynamics of the environment can change over time. Reinforcement Learning (RL), a popular approach for DMU problems, learns a policy by interacting with a model of the environment offline. Unfortunately, if the environment changes the policy can become stale and take sub-optimal actions, and relearning the policy for the updated environment takes time and computational effort. An alternative is online planning approaches such as Monte Carlo Tree Search (MCTS), which perform their computation at decision time. Given the current environment, MCTS plans using high-fidelity models to determine promising action trajectories. These models can be updated as soon as environmental changes are detected to immediately incorporate them into decision making. However, MCTS's convergence can be slow for domains with large state-action spaces. In this paper, we present a novel hybrid decision-making approach that combines the strengths of RL and planning while mitigating their weaknesses. Our approach, called Policy Augmented MCTS (PA-MCTS), integrates a policy's actin-value estimates into MCTS, using the estimates to seed the action trajectories favored by the search. We hypothesize that PA-MCTS will converge more quickly than standard MCTS while making better decisions than the policy can make on its own when faced with nonstationary environments. We test our hypothesis by comparing PA-MCTS with pure MCTS and an RL agent applied to the classical CartPole environment. We find that PC-MCTS can achieve higher cumulative rewards than the policy in isolation under several environmental shifts while converging in significantly fewer iterations than pure MCTS.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Designing Decision Support Systems for Emergency Response: Challenges and Opportunities

Designing effective emergency response management (ERM) systems to respond to incidents such as road accidents is a major problem faced by communities. In addition to responding to frequent incidents each day (about 240 million emergency medical services calls and over 5 million road accidents in the US each year), these systems also support response during natural hazards. Recently, there has been a consistent interest in building decision support and optimization tools that can help emergency responders provide more efficient and effective response. This includes a number of principled subsystems that implement early incident detection, incident likelihood forecasting and strategic resource allocation and dispatch policies. In this paper, we highlight the key challenges and provide an overview of the approach developed by our team in collaboration with our community partners.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Generative Anomaly Detection for Time Series Datasets

Traffic congestion anomaly detection is of paramount importance in intelligent traffic systems. The goals of transportation agencies are two-fold: to monitor the general traffic conditions in the area of interest and to locate road segments under abnormal congestion states. Modeling congestion patterns can achieve these goals for citywide roadways, which amounts to learning the distribution of multivariate time series (MTS). However, existing works are either not scalable or unable to capture the spatial-temporal information in MTS simultaneously. To this end, we propose a principled and comprehensive framework consisting of a data-driven generative approach that can perform tractable density estimation for detecting traffic anomalies. Our approach first clusters segments in the feature space and then uses conditional normalizing flow to identify anomalous temporal snapshots at the cluster level in an unsupervised setting. Then, we identify anomalies at the segment level by using a kernel density estimator on the anomalous cluster. Extensive experiments on synthetic datasets show that our approach significantly outperforms several state-of-the-art congestion anomaly detection and diagnosis methods in terms of Recall and F1-Score. We also use the generative model to sample labeled data, which can train classifiers in a supervised setting, alleviating the lack of labeled data for anomaly detection in sparse settings.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Holographic spacetime, black holes and quantum error correcting codes: A review

This article reviews the progress in our understanding of the reconstruction of the bulk spacetime in the holographic correspondence from the dual field theory including an account of how these developments have led to the reproduction of the Page curve of the Hawking radiation from black holes. We review quantum error correction and relevant recovery maps with toy examples based on tensor networks, and discuss how it provides the desired framework for bulk reconstruction in which apparent inconsistencies with properties of the operator algebra in the dual field theory are naturally resolved. The importance of understanding the modular flow in the dual field theory has been emphasized. We discuss how the state-dependence of reconstruction of black hole microstates can be formulated in the framework of quantum error correction with inputs from extremal surfaces along with a quantification of the complexity of encoding of bulk operators. Finally, we motivate and discuss a class of tractable microstate models of black holes which can illuminate how the black hole complementarity principle can emerge operationally without encountering information paradoxes, and provide new insights into generation of desirable features of encoding into the Hawking radiation.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Offline Vehicle Routing Problem with Online Bookings: A Novel Problem Formulation with Applications to Paratransit

Vehicle routing problems (VRPs) can be divided into two major categories: offline VRPs, which consider a given set of trip requests to be served, and online VRPs, which consider requests as they arrive in real-time. Based on discussions with public transit agencies, we identify a real-world problem that is not addressed by existing formulations: booking trips with flexible pickup windows (e.g., 3 hours) in advance (e.g., the day before) and confirming tight pickup windows (e.g., 30 minutes) at the time of booking. Such a service model is often required in paratransit service settings, where passengers typically book trips for the next day over the phone. To address this gap between offline and online problems, we introduce a novel formulation, the offline vehicle routing problem with online bookings. This problem is very challenging computationally since it faces the complexity of considering large sets of requests -- similar to offline VRPs -- but must abide by strict constraints on running time -- similar to online VRPs. To solve this problem, we propose a novel computational approach, which combines an anytime algorithm with a learning-based policy for real-time decisions. Based on a paratransit dataset obtained from the public transit agency of Chattanooga, TN, we demonstrate that our novel formulation and computational approach lead to significantly better outcomes in this setting than existing algorithms.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Quantum thermodynamics of holographic quenches and bounds on the growth of entanglement from the QNEC

The quantum null energy condition (QNEC) is a lower bound on the energy-momentum tensor in terms of the variation of the entanglement entropy of a sub-region along a null direction. To gain insights into quantum thermodynamics of many-body systems, we study if the QNEC restricts irreversible entropy production in quenches driven by energy-momentum inflow from an infinite memoryless bath in two-dimensional holographic theories. We find that an increase in both entropy and temperature, as implied by the Clausius inequality of classical thermodynamics, are necessary but not sufficient to not violate QNEC in quenches leading to transitions between thermal states with momentum which are dual to Banados-Teitelboim-Zanelli geometries. For an arbitrary initial state, we can determine the lower and upper bounds on the increase of entropy (temperature) for a fixed increase in temperature (entropy). Our results provide explicit instances of quantum lower and upper bounds on irreversible entropy production whose existence has been established in literature. We also find monotonic behavior of the non-saturation of the QNEC with time after a quench, and analytically determine their asymptotic values. Our study shows that the entanglement entropy of an interval of length $l$ always thermalizes in time $l/2$ with an exponent $3/2$. Furthermore, we determine the coefficient of initial quadratic growth of entanglement analytically for any $l$, and show that the slope of the asymptotic ballistic growth of entanglement for a semi-infinite interval is twice the difference of the entropy densities of the final and initial states. We determine explicit upper and lower bounds on these rates of growth of entanglement.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Hierarchical Planning for Resource Allocation in Emergency Response Systems

A classical problem in city-scale cyber-physical systems (CPS) is resource allocation under uncertainty. Typically, such problems are modeled as Markov (or semi-Markov) decision processes. While online, offline, and decentralized approaches have been applied to such problems, they have difficulty scaling to large decision problems. We present a general approach to hierarchical planning that leverages structure in city-level CPS problems for resource allocation under uncertainty. We use the emergency response as a case study and show how a large resource allocation problem can be split into smaller problems. We then create a principled framework for solving the smaller problems and tackling the interaction between them. Finally, we use real-world data from Nashville, Tennessee, a major metropolitan area in the United States, to validate our approach. Our experiments show that the proposed approach outperforms state-of-the-art approaches used in the field of emergency response.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Hydrodynamic attractor of a hybrid viscous fluid in Bjorken flow

The nonequilibrium evolution in a boost-invariant Bjorken flow of a hybrid viscous fluid model containing two interacting components with different viscosities, such that they represent strongly and weakly self-coupled sectors, is shown to be characterized by a hydrodynamic attractor which has an early-time behavior that is reminiscent of the so-called bottom-up thermalization scenario in heavy-ion collisions. The hydrodynamization times for the two sectors can differ strongly, with details depending on the curve realized on the two-dimensional attractor surface, which might account for different scenarios for small and large systems in nuclear collisions. The total system behaves like a single viscous fluid with a dynamically determined effective shear viscosity.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

On Algorithmic Decision Procedures in Emergency Response Systems in Smart and Connected Communities

Emergency Response Management (ERM) is a critical problem faced by communities across the globe. Despite this, it is common for ERM systems to follow myopic decision policies in the real world. Principled approaches to aid ERM decision-making under uncertainty have been explored but have failed to be accepted into real systems. We identify a key issue impeding their adoption --- algorithmic approaches to emergency response focus on reactive, post-incident dispatching actions, i.e. optimally dispatching a responder \textit{after} incidents occur. However, the critical nature of emergency response dictates that when an incident occurs, first responders always dispatch the closest available responder to the incident. We argue that the crucial period of planning for ERM systems is not post-incident, but between incidents. This is not a trivial planning problem --- a major challenge with dynamically balancing the spatial distribution of responders is the complexity of the problem. An orthogonal problem in ERM systems is planning under limited communication, which is particularly important in disaster scenarios that affect communication networks. We address both problems by proposing two partially decentralized multi-agent planning algorithms that utilize heuristics and exploit the structure of the dispatch problem. We evaluate our proposed approach using real-world data, and find that in several contexts, dynamic re-balancing the spatial distribution of emergency responders reduces both the average response time as well as its variance.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Time-dependent $NAdS_2$ holography with applications

We develop a method for obtaining exact time-dependent solutions in Jackiw-Teitelboim gravity coupled to non-conformal matter and study consequences for $NAdS_2$ holography. We study holographic quenches in which we find that the black hole mass increases. A semi-holographic model composed of an infrared $NAdS_2$ holographic sector representing the mutual strong interactions of trapped impurities confined at a spatial point is proposed. The holographic sector couples to the position of a displaced impurity acting as a self-consistent boundary source. This effective $0+1-$dimensional description has a total conserved energy. Irrespective of the initial velocity of the particle, the black hole mass initially increases, but after the horizon runs away to infinity in the physical patch, the mass vanishes in the long run. The total energy is completely transferred to the kinetic energy or the self-consistent confining potential energy of the impurity. For initial velocities below a critical value determined by the mutual coupling, the black hole mass changes sign in finite time. Above this critical velocity, the initial condition of the particle can be retrieved from the $SL(2,R)$ invariant exponent that governs the exponential growth of the bulk gravitational $SL(2,R)$ charges at late time.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Holography as a highly efficient RG flow I: Rephrasing gravity

We investigate how the holographic correspondence can be reformulated as a generalisation of Wilsonian RG flow in a strongly interacting large $N$ quantum field theory. We firstly define a \textit{highly efficient RG flow} as one in which the Ward identities related to local conservation of energy, momentum and charges preserve the same form at each scale -- to achieve this it is necessary to redefine the background metric and external sources at each scale as functionals of the effective single trace operators. These redefinitions also absorb the contributions of the multi-trace operators to these effective Ward identities. Thus the background metric and external sources become effectively dynamical reproducing the dual classical gravity equations in one higher dimension. Here, we focus on reconstructing the pure gravity sector as a highly efficient RG flow of the energy-momentum tensor operator, leaving the explicit constructive field theory approach for generating such RG flows to the second part of the work. We show that special symmetries of the highly efficient RG flows carry information through which we can decode the gauge fixing of bulk diffeomorphisms in the corresponding gravity equations. We also show that the highly efficient RG flow which reproduces a given classical gravity theory in a given gauge is \textit{unique} provided the endpoint can be transformed to a non-relativistic fixed point with a finite number of parameters under a universal rescaling. The results obtained here are used in the second part of this work, where we do an explicit field-theoretic construction of the RG flow, and obtain the dual classical gravity theory.

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preprint2016arXiv

Holography as a highly efficient RG flow II: An explicit construction

We complete the reformulation of the holographic correspondence as a \emph{highly efficient RG flow} that can also determine the UV data in the field theory in the strong coupling and large $N$ limit. We introduce a special way to define operators at any given scale in terms of appropriate coarse-grained collective variables, without requiring the use of the elementary fields. The Wilsonian construction is generalised by promoting the cut-off to a functional of these collective variables. We impose three criteria to determine the coarse-graining. The first criterion is that the effective Ward identities for local conservation of energy, momentum, etc. should preserve their standard forms, but in new scale-dependent background metric and sources which are functionals of the effective single trace operators. The second criterion is that the scale-evolution equations of the operators in the actual background metric should be state-independent, implying that the collective variables should not explicitly appear in them. The final criterion is that the endpoint of the scale-evolution of the RG flow can be transformed to a fixed point corresponding to familiar non-relativistic equations with a finite number of parameters, such as incompressible non-relativistic Navier-Stokes, under a certain universal rescaling of the scale and of the time coordinate. Using previous work, we explicitly show that in the hydrodynamic limit each such highly efficient RG flow reproduces a unique classical gravity theory with precise UV data that satisfy our IR criterion. We obtain the explicit coarse-graining which reproduces Einstein's equations. In a simple example, we are also able to compute the beta function. Finally, we show how our construction can be interpolated with the traditional Wilsonian RG flow at a suitable scale, and can be used to develop new non-perturbative frameworks for QCD-like theories.

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preprint2016arXiv

Semi-Holography for Heavy Ion Collisions: Self-Consistency and First Numerical Tests

We present an extended version of a recently proposed semi-holographic model for heavy-ion collisions, which includes self-consistent couplings between the Yang-Mills fields of the Color Glass Condensate framework and an infrared AdS/CFT sector, such as to guarantee the existence of a conserved energy-momentum tensor for the combined system that is local in space and time, which we also construct explicitly. Moreover, we include a coupling of the topological charge density in the glasma to the same of the holographic infrared CFT. The semi-holographic approach makes it possible to combine CGC initial conditions and weak-coupling glasma field equations with a simultaneous evolution of a strongly coupled infrared sector describing the soft gluons radiated by hard partons. As a first numerical test of the semi-holographic model we study the dynamics of fluctuating homogeneous color-spin-locked Yang-Mills fields when coupled to a homogeneous and isotropic energy-momentum tensor of the holographic IR-CFT, and we find rapid convergence of the iterative numerical procedure suggested earlier.

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preprint2016arXiv

Time-dependence of the holographic spectral function: Diverse routes to thermalisation

We develop a new method for computing the holographic retarded propagator in generic (non-)equilibrium states using the state/geometry map. We check that our method reproduces the thermal spectral function given by the Son-Starinets prescription. The time-dependence of the spectral function of a relevant scalar operator is studied in a class of non-equilibrium states. The latter are represented by AdS-Vaidya geometries with an arbitrary parameter characterising the timescale for the dual state to transit from an initial thermal equilibrium to another due to a homogeneous quench. For long quench duration, the spectral function indeed follows the thermal form at the instantaneous effective temperature adiabatically, although with a slight initial time delay and a bit premature thermalisation. At shorter quench durations, several new non-adiabatic features appear: (i) time-dependence of the spectral function is seen much before than that in the effective temperature (advanced time-dependence), (ii) a big transfer of spectral weight to frequencies greater than the initial temperature occurs at an intermediate time (kink formation) and (iii) new peaks with decreasing amplitudes but in greater numbers appear even after the effective temperature has stabilised (persistent oscillations). We find four broad routes to thermalisation for lower values of spatial momenta. At higher values of spatial momenta, kink formations and persistent oscillations are suppressed, and thermalisation time decreases. The general thermalisation pattern is globally top-down, but a closer look reveals complexities.

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preprint2015arXiv

A semi-holographic model for heavy-ion collisions

We develop a semi-holographic model for the out-of-equilibrium dynamics during the partonic stages of an ultrarelativistic heavy-ion collision. The model combines a weakly-coupled hard sector, involving gluon modes with energy and momenta of the order of the saturation momentum and relatively large occupation numbers, with a strongly-coupled soft sector, which physically represents the soft gluons radiated by the hard partons. The hard sector is described by perturbative QCD, more precisely, by its semi-classical approximation (the classical Yang-Mills equations) which becomes appropriate when the occupation numbers are large. The soft sector is described by a marginally deformed conformal field theory, which in turn admits a holographic description in terms of classical Einstein's equations in $AdS_5$ with a minimally coupled massless `dilaton'. The model involve two free parameters which characterize the gauge-invariant couplings between the hard and soft sectors. Via these couplings, the hard modes provide dynamical sources for the gravitational equations at the boundary of $AdS_5$ and feel the feedback of the latter as additional soft sources in the classical Yang-Mills equations. Importantly, the initial conditions for this coupled dynamics are fully determined by the hard sector alone, i.e. by perturbative QCD, and are conveniently given by the color glass condensate (CGC) effective theory. We also develop a new semi-holographic picture of jets in the QGP by attaching a non-Abelian charge to the endpoint of the trailing string in $AdS_5$ representing a heavy quark. This leads to modified Nambu-Goto equations for the string which govern the (collisional and radiative) energy loss by the heavy quark towards both hard and soft modes.

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preprint2014arXiv

Holographic perfect fluidity, Cotton energy-momentum duality and transport properties

We investigate background metrics for 2+1-dimensional holographic theories where the equilibrium solution behaves as a perfect fluid, and admits thus a thermodynamic description. We introduce stationary perfect-Cotton geometries, where the Cotton--York tensor takes the form of the energy--momentum tensor of a perfect fluid, i.e. they are of Petrov type D_t. Fluids in equilibrium in such boundary geometries have non-trivial vorticity. The corresponding bulk can be exactly reconstructed to obtain 3+1-dimensional stationary black-hole solutions with no naked singularities for appropriate values of the black-hole mass. It follows that an infinite number of transport coefficients vanish for holographic fluids. Our results imply an intimate relationship between black-hole uniqueness and holographic perfect equilibrium. They also point towards a Cotton/energy--momentum tensor duality constraining the fluid vorticity, as an intriguing boundary manifestation of the bulk mass/nut duality.

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preprint2014arXiv

Phenomenological characterisation of semi-holographic non-Fermi liquids

We analyse some phenomenological implications of the most general semi-holographic models for non-Fermi liquids that have emerged with inputs from the holographic correspondence. We find generalizations of Landau-Silin equations with few parameters governing thermodynamics, low energy response and collective excitations. We show that even when there is a Fermi surface with well-defined quasi-particle excitations, the collective excitations can behave very differently from Landau's theory.

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preprint2013arXiv

Non-equilibrium fluctuation-dissipation relation from holography

We derive a non-equilibrium fluctuation-dissipation relation for bosonic correlation functions from holography in the classical gravity approximation at strong coupling. This generalizes the familiar thermal fluctuation-dissipation relation in absence of external sources. This also holds universally for any non-equilibrium state which can be obtained from a stable thermal equilibrium state in perturbative derivative (hydrodynamic) and amplitude (non-hydrodynamic) expansions. Therefore, this can provide a strong experimental test for the applicability of the holographic framework. We discuss how it can be tested in heavy ion collisions. We also make a conjecture regarding multi-point holographic non-equilibrium Green's functions.

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preprint2013arXiv

Spacetime emergence via holographic RG flow from incompressible Navier-Stokes at the horizon

We show that holographic RG flow can be defined precisely such that it corresponds to emergence of spacetime. We consider the case of pure Einstein's gravity with a negative cosmological constant in the dual hydrodynamic regime. The holographic RG flow is a system of first order differential equations for radial evolution of the energy-momentum tensor and the variables which parametrize it's phenomenological form on hypersurfaces in a foliation. The RG flow can be constructed without explicit knowledge of the bulk metric provided the hypersurface foliation is of a special kind. The bulk metric can be reconstructed once the RG flow equations are solved. We show that the full spacetime can be determined from the RG flow by requiring that the horizon fluid is a fixed point in a certain scaling limit leading to the non-relativistic incompressible Navier-Stokes dynamics. This restricts the near-horizon forms of all transport coefficients, which are thus determined independently of their asymptotic values and the RG flow can be solved uniquely. We are therefore able to recover the known boundary values of almost all transport coefficients at the first and second orders in the derivative expansion. We conjecture that the complete characterisation of the general holographic RG flow, including the choice of counterterms, might be determined from the hydrodynamic regime.

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preprint2012arXiv

The holographic spectral function in non-equilibrium states

We develop holographic prescriptions for obtaining spectral functions in non-equilibrium states and space-time dependent non-equilibrium shifts in the energy and spin of quasi-particle like excitations. We reproduce strongly coupled versions of aspects of non-equilibrium dynamics of Fermi surfaces in Landau's Fermi-liquid theory. We find that the incoming wave boundary condition at the horizon does not suffice to obtain a well-defined perturbative expansion for non-equilibrium observables. Our prescription, based on analysis of regularity at the horizon, allows such a perturbative expansion to be achieved nevertheless and can be precisely formulated in a universal manner independent of the non-equilibrium state, provided the state thermalizes. We also find that the non-equilibrium spectral function furnishes information about the relaxation modes of the system. Along the way, we argue that in a typical non-supersymmetric theory with a gravity dual, there may exist a window of temperature and chemical potential at large N, in which a generic non-equilibrium state can be characterized by just a finitely few operators with low scaling dimensions, even far away from the hydrodynamic limit.

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preprint2011arXiv

Homogeneous Relaxation at Strong Coupling from Gravity

Homogeneous relaxation is a ubiquitous phenomenon in semiclassical kinetic theories where the quasiparticles are distributed uniformly in space, and the equilibration involves only their velocity distribution. For such solutions, the hydrodynamic variables remain constant. We construct asymptotically AdS solutions of Einstein's gravity dual to such processes at strong coupling, perturbatively in the amplitude expansion, where the expansion parameter is the ratio of the amplitude of the non-hydrodynamic shear-stress tensor to the pressure. At each order, we sum over all time derivatives through exact recursion relations. We argue that the metric has a regular future horizon, order by order in the amplitude expansion, provided the shear-stress tensor follows an equation of motion. At the linear order, this equation of motion implies that the metric perturbations are composed of zero wavelength quasinormal modes. Our method allows us to calculate the non-linear corrections to this equation perturbatively in the amplitude expansion. We thus derive a special case of our previous conjecture on the regularity condition on the boundary stress tensor that endows the bulk metric with a regular future horizon, and also refine it further. We also propose a new outlook for heavy-ion phenomenology at RHIC and ALICE.

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preprint2011arXiv

Phenomenology of Irreversible Processes from Gravity

We propose that the space-time evolution of strongly coupled matter formed by ultra-relativistic heavy ion collisions can be modelled by phenomenological equations involving the energy-momentum tensor and conserved currents alone. These equations can describe the late stage of local chemical and thermal equilibration of the matter formed after collisions, and its subsequent transition to hydrodynamic expansion in an unified framework. The full set of equations include local energy, momentum and charge conservation; but also additional equations for evolution of non-equilibrium variables. These equations with precisely determined phenomenological parameters can be obtained by the AdS/CFT correspondence. On the gravity side of this correspondence, for vanishing chemical potentials, these phenomenological equations give all solutions of pure gravity in AdS which have regular future horizons. We also discuss field-theoretic grounds for validity of these phenomenological equations.

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preprint2011arXiv

The unconditional RG flow of the relativistic holographic fluid

We study asymptotically slowly varying perturbations of the AdS black brane in Einstein's gravity with a negative cosmological constant. We allow both the induced metric and the Brown-York stress tensor at a given radial cut-off slice to fluctuate. These fluctuations, which determine the radial evolution of the metric, are parametrized in terms of boundary data. We observe that the renormalized energy-momentum tensor at any radial slice takes the standard hydrodynamic form which is relativistically covariant with respect to the induced metric. The RG flow of the fluid takes the form of field redefinitions of the boundary hydrodynamic variables. To show this, up to first order in the derivative expansion, we only need to investigate the radial flow of the boundary data and do not need to impose constraints on them. Imposing the constraints gives unforced nonlinear hydrodynamic equations at any radial slice. Along the way we make a careful study of the choice of counter-terms and hypersurfaces involved in defining the holographic RG flow, while at the same time we do not explicitly set any boundary condition either at the cut-off or at the horizon. We find that η/s does not change along the RG flow, equaling 1/(4π) when the future horizon is regular. We also analyze the flow of the speed of sound and find that it diverges at the horizon.

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preprint2010arXiv

An AdS/CFT Connection between Boltzmann and Einstein

The AdS/CFT correspondence defines a sector with universal strongly coupled dynamics in the field theory as the dual of pure gravity in AdS described by Einstein's equation with a negative cosmological constant. We explain here, from the field-theoretic viewpoint how the dynamics in this sector gets determined by the expectation value of the energy-momentum tensor \emph{alone}. We first show that the Boltzmann equation has very special solutions which could be \textit{functionally} completely determined in terms of the energy-momentum tensor alone. We call these solutions \textit{conservative solutions}. We indicate why conservative solutions should also exist when we refine this kinetic description to go closer to the exact microscopic theory or even move away from the regime of weak coupling so that no kinetic description could be employed. We argue that these \textit{conservative solutions} form the universal sector dual to pure gravity at strong coupling and large $N$. Based on this observation, we propose a \textit{regularity condition} on the energy-momentum tensor so that the dual solution in pure gravity has a smooth future horizon. We also study if irreversibility emerges only at long time scales of observation, unlike the case of the Boltzmann equation.

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preprint2009arXiv

A Covariant Form of the Navier-Stokes Equation for the Galilean Conformal Algebra

We demonstrate that the Navier-Stokes equation can be covariantized under the full infinite dimensional Galilean Conformal Algebra (GCA), such that it reduces to the usual Navier-Stokes equation in an inertial frame. The covariantization is possible only for incompressible flows, i.e when the divergence of the velocity field vanishes. Using the continuity equation, we can fix the transformation of pressure and density under GCA uniquely. We also find that when all chemical potentials vanish, $c_{s}$, which denotes the speed of sound in an inertial frame comoving with the flow, must either be a fundamental constant or given in terms of microscopic parameters. We will discuss how both could be possible. In absence of chemical potentials, we also find that the covariance under GCA implies that either the viscosity should vanish or the microscopic theory should have a length scale or a time scale or both. We further find that the higher derivative corrections to the Navier-Stokes equation, can be covariantized, only if they are restricted to certain possible combinations in the inertial frame. We explicitly evaluate all possible three derivative corrections. Finally, we argue that our analysis hints that the parent relativistic theory with relativistic conformal symmetry needs to be deformed before the contraction is taken to produce a sensible GCA invariant dynamical limit.

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preprint2008arXiv

Worldsheet Properties of Extremal Correlators in AdS/CFT

We continue to investigate planar four point worldsheet correlators of string theories which are conjectured to be duals of free gauge theories. We focus on the extremal correlators <Tr(Z^{J_1}(x)) Tr(Z^{J_2}(y)) Tr(Z^{J_3}(z)) Tr(\bar{Z}^{J}(0))> of $N = 4$ SYM theory, and construct the corresponding worldsheet correlators in the limit when the $J_i >> 1$. The worldsheet correlator gets contributions, in this limit, from a whole family of Feynman graphs. We find that it is supported on a {\it curve} in the moduli space parametrised by the worldsheet crossratio. In a further limit of the spacetime correlators we find this curve to be the unit circle. In this case, we also check that the entire worldsheet correlator displays the appropriate crossing symmetry. The non-renormalization of the extremal correlators in the 't Hooft coupling offers a potential window for a comparison of these results with those from strong coupling.

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