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Charged Magnetic Brane Correlators and Twisted Virasoro Algebras

Prior work using gauge/gravity duality has established the existence of a quantum critical point in the phase diagram of 3+1-dimensional gauge theories at finite charge density and background magnetic field. The critical theory, obtained by tuning the dimensionless charge density to magnetic field ratio, exhibits nontrivial scaling in its thermodynamic properties, and an associated nontrivial dynamical critical exponent. In the present work, we analytically compute low energy correlation functions in the background of the charged magnetic brane solution to 4+1-dimensional Einstein-Maxwell-Chern-Simons theory, which represents the bulk description of the critical point. Results are obtained for neutral scalar operators, the stress tensor, and the U(1)-current. The theory is found to exhibit a twisted Virasoro algebra, constructed from a linear combination of the original stress tensor and chiral U(1)-current. The effective speed of light in the IR is renormalized downward for one chirality, but not the other, by finite density, a behavior that is consistent with a Luttinger liquid description of fermions in the lowest Landau level. The results obtained here do not directly shed light on the mechanism driving the phase transition, and we comment on why this is so.