In three Lifshitz-like black brane models, the null energy condition and third law of thermodynamics show no correlation in two cases but the former implies the latter in the third.
Charged Magnetic Brane Solutions in AdS_5 and the fate of the third law of thermodynamics
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abstract
We construct asymptotically AdS_5 solutions to 5-dimensional Einstein-Maxwell theory with Chern-Simons term which are dual to 4-dimensional gauge theories, including N=4 SYM theory, in the presence of a constant background magnetic field B and a uniform electric charge density \rho. For the solutions corresponding to supersymmetric gauge theories, we find numerically that a small magnetic field causes a drastic decrease in the entropy at low temperatures. The near-horizon AdS_2 \times R^3 geometry of the purely electrically charged brane thus appears to be unstable under the addition of a small magnetic field. Based on this observation, we propose a formulation of the third law of thermodynamics (or Nernst theorem) that can be applied to black holes in the AdS/CFT context. We also find interesting behavior for smaller, non-supersymmetric, values of the Chern-Simons coupling k. For k=1 we exhibit exact solutions corresponding to warped AdS_3 black holes, and show that these can be connected to asymptotically AdS_5 spacetime. For k\leq 1 the entropy appears to go to a finite value at extremality, but the solutions still exhibit a mild singularity at strictly zero temperature. In addition to our numerics, we carry out a complete perturbative analysis valid to order B^2, and find that this corroborates our numerical results insofar as they overlap.
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Generalizes the holographic prescription for fermionic retarded Green's functions to anisotropic geometries and numerically evaluates direction-dependent features, instabilities, Landau levels, and a pseudogap in three specific models.
Holographic entanglement entropy exhibits a swallow-tail structure indicating connected-to-disconnected transitions for perpendicular magnetic fields in the QCD phase diagram while remaining monotonic for parallel fields, consistent with black hole thermodynamics.
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Lifshitz-like Magnetic Black Branes: Third Law of Thermodynamics and the Null Energy Condition
In three Lifshitz-like black brane models, the null energy condition and third law of thermodynamics show no correlation in two cases but the former implies the latter in the third.
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Holographic correlation functions of fermions in anisotropic plasma
Generalizes the holographic prescription for fermionic retarded Green's functions to anisotropic geometries and numerically evaluates direction-dependent features, instabilities, Landau levels, and a pseudogap in three specific models.
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Holographic entanglement entropy in the QCD phase diagram under external magnetic field
Holographic entanglement entropy exhibits a swallow-tail structure indicating connected-to-disconnected transitions for perpendicular magnetic fields in the QCD phase diagram while remaining monotonic for parallel fields, consistent with black hole thermodynamics.
- Lifshitz-like black branes in arbitrary dimensions and the third law of thermodynamics