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arXiv · 1810.07267

Negative specific heat from non-planar interactions and small black holes in AdS/CFT

David Berenstein
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Abstract

The gravity side of the gauge/gravity duality predicts the existence of small black holes with negative specific heat. A free theory of strings has a Hagedorn behavior, but it does not lead to negative specific heat. To understand such states one needs to consider a theory of interacting strings. In the dual gauge theory, the string interactions are related to non-planar diagrams. In this paper the simplest gauge matrix model of two free matrices, that has Hagedorn behavior is analyzed in detail. A simple double trace deformation of the Hamiltonian, proportional to square of the free Hamiltonian square with a negative sign that mimics a gravitational attraction is enough to produce states with negative specific heat perturbatively and one can still compute the equation of state relating the entropy and the energy. A more general argument based on non-planar interactions that are random and that grow faster in strength than the energy suggests that states with negative specific heat appear generically.

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David Berenstein. 2018-12-13. Negative specific heat from non-planar interactions and small black holes in AdS/CFT. https://doi.org/10.1007/jhep10(2019)001

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