Charged Magnetic Brane Solutions in AdS_5 and the fate of the third law of thermodynamics

Understand

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.