Negative specific heat from nonplanar 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 nonplanar 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 nonplanar interactions that are random and that grow faster in strength than the energy suggests that states with negative specific heat appear generically.
 Authors:

 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 10298479
 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 nonplanar interactions and small black holes in AdS/CFT. United States: N. p., 2019.
Web. https://doi.org/10.1007/JHEP10(2019)001.
Berenstein, David. Negative specific heat from nonplanar interactions and small black holes in AdS/CFT. United States. https://doi.org/10.1007/JHEP10(2019)001
Berenstein, David. Thu .
"Negative specific heat from nonplanar 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.
@article{osti_1602234,
title = {Negative specific heat from nonplanar 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 nonplanar 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 nonplanar 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}
}
Web of Science
Works referenced in this record:
Building up spacetime with quantum entanglement
journal, June 2010
 Van Raamsdonk, Mark
 General Relativity and Gravitation, Vol. 42, Issue 10
Antide Sitter space, thermal phase transition, and confinement in gauge theories
journal, January 1998
 Witten, Edward
 Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 3
Black strings and p branes are unstable
journal, May 1993
 Gregory, Ruth; Laflamme, Raymond
 Physical Review Letters, Vol. 70, Issue 19
`Doubletrace' deformations, boundary conditions and spacetime singularities
journal, May 2002
 Berkooz, Micha; Sever, Amit; Shomer, Assaf
 Journal of High Energy Physics, Vol. 2002, Issue 05
Eternal black holes in antide Sitter
journal, April 2003
 Maldacena, Juan
 Journal of High Energy Physics, Vol. 2003, Issue 04
Submatrix deconfinement and small black holes in AdS
journal, September 2018
 Berenstein, David
 Journal of High Energy Physics, Vol. 2018, Issue 9
Invasion of the giant gravitons from antide Sitter space
journal, May 2000
 McGreevy, John; Susskind, Leonard; Toumbas, Nicolaos
 Journal of High Energy Physics, Vol. 2000, Issue 06
Thermodynamics of black holes in antide Sitter space
journal, December 1983
 Hawking, S. W.; Page, Don N.
 Communications in Mathematical Physics, Vol. 87, Issue 4
Thermal properties of a string bit model at large N
journal, October 2017
 Beccaria, Matteo
 Journal of High Energy Physics, Vol. 2017, Issue 10
AdS _{3} black holes and a stringy exclusion principle
journal, December 1998
 Maldacena, Juan; Strominger, Andrew
 Journal of High Energy Physics, Vol. 1998, Issue 12
A matrix model for the twodimensional black hole
journal, February 2002
 Kazakov, Vladimir; Kostov, Ivan K.; Kutasov, David
 Nuclear Physics B, Vol. 622, Issue 12
Small AdS black holes from SYM
journal, March 2009
 Asplund, Curtis; Berenstein, David
 Physics Letters B, Vol. 673, Issue 45
Singularities and closed timelike curves in typeIIB 1/2 BPS geometries
journal, September 2005
 Milanesi, Giuseppe; O'Loughlin, Martin
 Journal of High Energy Physics, Vol. 2005, Issue 09
The Hagedorn/Deconfinement Phase Transition in Weakly Coupled Large N Gauge Theories
journal, January 2004
 Aharony, Ofer; Marsano, Joseph; Minwalla, Shiraz
 Advances in Theoretical and Mathematical Physics, Vol. 8, Issue 4
Chronology protection in antide Sitter
journal, August 2005
 Caldarelli, Marco M.; Klemm, Dietmar; Silva, Pedro J.
 Classical and Quantum Gravity, Vol. 22, Issue 17