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arXiv 0911.4518hep-th
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AdS_5中的带电磁膜溶液和热力学第三定律的命运

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

Eric D'Hoker, Per Kraus

摘要:

在恒定背景磁场B和均匀电荷密度ρ存在的情况下,我们构造了具有Chern-Simons项的5维Einstein-Maxwell理论的渐近AdS_5解,该解与包括N=4 SYM理论在内的4维规范理论是对偶的.对于对应于超对称规范理论的解,我们用数值计算的方法发现,在低温下,一个小的磁场会引起熵的急剧下降。因此,纯带电膜的近视界AdS_2 \times R^3几何结构在外加小磁场时似乎是不稳定的。基于这一观察,我们提出了热力学第三定律(或能斯特定理),可以适用于黑洞在AdS/CFT的背景下制定。我们还发现有趣的行为较小,非超对称,值的陈-西蒙斯耦合k。对于k=1,我们展示了对应于扭曲的AdS_3黑洞的精确解,并表明这些可以连接到渐近AdS_5时空。对于k \leq 1的熵似乎去到一个极值,但解决方案仍然表现出温和的奇异性在严格的零温度。除了我们的数值计算之外,我们还进行了一个完整的微扰分析,对B^2阶有效,并且发现这证实了我们的数值计算结果,只要它们重叠。

英文摘要:

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 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 \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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