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Magnetic Critical Solutions in Holography

The AdS/CFT correspondence is a realization of the holographic principle in the context of string theory. It is a map between a quantum field theory and a string theory living in one or more extra dimensions. Holography provides new tools to study strongly-coupled quantum field theories. It has important applications in quantum chromodynamics (QCD) and condensed matter (CM) systems, which are usually complicated and strongly coupled. Quantum critical CM theories have scaling symmetries and can be connected to higher-dimensional scale invariant space-times. The Effective Holographic Theory paradigm may be used to describe the low-energy (IR) holographic dynamics of quantum critical systems by the Einstein-Maxwell-Dilaton (EMD) theory. We find the magnetic critical scaling solutions of an EMD theory containing an extra parity-odd term $F\wedge F$. Previous studies in the absence of magnetic fields have shown the existence of quantum critical lines separated by quantum critical points. We find this is also true in the presence of a magnetic field. The critical solutions are characterized by the triplet of critical exponents ($θ,z,ζ$), the first two describing the geometry, while the latter describes the charge density.