Abstract
We construct asymptotically AdS5 solutions to 5-dimensional Einstein-Maxwell theory with Chern-Simons term which are dual to 4-dimensional gauge theories, including \(\mathcal{N} = 4 \) SYM theory, in the presence of a constant background magnetic field B and a uniform electric charge density ρ. 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 AdS2 × 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 AdS3 black holes, and show that these can be connected to asymptotically AdS5 spacetime. For k ≤ 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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ArXiv ePrint: 0911.4518
1This work was supported in part by NSF grant PHY-07-57702.
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D’Hoker, E., Kraus, P. Charged magnetic brane solutions in AdS5 and the fate of the third law of thermodynamics. J. High Energ. Phys. 2010, 95 (2010). https://doi.org/10.1007/JHEP03(2010)095
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DOI: https://doi.org/10.1007/JHEP03(2010)095