Charged magnetic brane solutions in AdS5 and the fate of the third law of thermodynamics

• Published in: The journal of high energy physics 2010-03, Vol.2010 (3), Article 95
• Main Authors: D’Hoker, Eric, Kraus, Per
• Format: Article
• Language: English
• Subjects: Asymptotic properties; Black holes; Charge density; Charging; Classical and Quantum Gravitation; Elementary Particles; Entropy; Exact solutions; High energy physics; Low temperature; Magnetic fields; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Relativity Theory; String Theory; Supersymmetry; Thermodynamics
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP03(2010)095

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 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 AdS 2 × 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 ≤ 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.