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

By E. D’Hoker, Per Kraus. 2009

165 citations recorded by the source corpus.

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 × R3 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 B2, and find that this corroborates our numerical results insofar as they overlap.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/82991f85a7e17668ac8572bfea761c4b634cf465

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In Astronomy and Astrophysics

1. S. Sachdev
2. Andrew Lucas
3. S. Hartnoll
4. Hirosi Ooguri
5. C. Park
6. Diego Trancanelli
7. V. Hubeny
8. D. Mateos

In Nuclear and High Energy Physics

1. S. Hartnoll
2. Andrew Lucas
3. S. Sachdev
4. Diego Trancanelli
5. Hirosi Ooguri
6. C. Park
7. V. Hubeny
8. T. Takayanagi

Citations in the corpus

• Thermodynamics and instabilities of a strongly coupled anisotropic plasma (2011, background): “s at nite temperature [10,11,12,13,14], gravity duals of p-wave superconductors[15,16,17,18, 19,20,21], solutions dual to N= 4 SYM theory coupled to electromagnetic elds with [22,23,24,25] or without [26,27] avour, and anisotropic solutions with singular horizons [28]. Part of the motivation for our”
• Holographic endpoint of spatially modulated phase transition (2010, background): “ent Jat the boundary. Because of the Chern-Simons term, the current is anomalous. We therefore treat the boundary gauge eld as an external and non-dynamical source as in recent 14 papers, for example [7, 8]. Note that the background solution we consider is inhomogeneous, carrying the momentum k. In ”
• Holographic Quantum Matter (2016, methodology): “This system has been studied in a series of papers including [197; 198; 199; 200].”