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

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.

Authors:
 [1]
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  1. Univ. of California, Santa Barbara, CA (United States)
Publication Date:
Research Org.:
Univ. of California, Santa Barbara, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1602234
Grant/Contract Number:  
SC0011702
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 10; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; black hole; gauge gravity correspondence; matrix models

Citation Formats

Berenstein, David. Negative specific heat from non-planar interactions and small black holes in AdS/CFT. United States: N. p., 2019. Web. doi:10.1007/JHEP10(2019)001.
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Berenstein, David. Negative specific heat from non-planar interactions and small black holes in AdS/CFT. United States. https://doi.org/10.1007/JHEP10(2019)001
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Berenstein, David. Thu . "Negative specific heat from non-planar interactions and small black holes in AdS/CFT". United States. https://doi.org/10.1007/JHEP10(2019)001. https://www.osti.gov/servlets/purl/1602234.
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@article{osti_1602234,
title = {Negative specific heat from non-planar interactions and small black holes in AdS/CFT},
author = {Berenstein, David},
abstractNote = {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.},
doi = {10.1007/JHEP10(2019)001},
journal = {Journal of High Energy Physics (Online)},
number = 10,
volume = 2019,
place = {United States},
year = {2019},
month = {10}
}
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https://doi.org/10.1007/JHEP10(2019)001
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