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

TL;DR

This paper investigates how non-planar interactions in a gauge matrix model can lead to the emergence of small black hole states with negative specific heat, aligning with predictions from gauge/gravity duality.

Contribution

It demonstrates that a simple double trace deformation in a free matrix model induces negative specific heat states, highlighting the role of non-planar interactions in black hole thermodynamics.

Findings

Negative specific heat states can be generated perturbatively in the matrix model.

Non-planar interactions grow faster than energy, leading to negative specific heat states.

The equation of state relating entropy and energy can be computed in this setup.

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.