A NOTE ON MATRIX MODEL WITH IR CUTOFF AND AdS/CFT

We study effective gauge theory at finite temperature on a three-sphere in the presence of an IR cutoff using AdS/CFT. Comparing with the thermodynamic behavior of its gravity dual, we analyze a phenomenological matrix model which describes the gauge theory in the strongly coupled regime. Subsequently, we study the behavior of the model as a function of the IR cutoff. We further argue that a similar matrix model represents the effective gauge theory on R3 with an IR-cutoff and analyze the model numerically.

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BLACK HOLE THERMODYNAMICS FROM CALCULATIONS IN STRONGLY COUPLED GAUGE THEORY

International Journal of Modern Physics A ◽

10.1142/s0217751x01003949 ◽

2001 ◽

Vol 16 (05) ◽

pp. 856-865 ◽

Cited By ~ 22

Author(s):

DANIEL KABAT ◽

GILAD LIFSCHYTZ ◽

DAVID LOWE

Keyword(s):

Black Hole ◽

Quantum Mechanics ◽

Gauge Theory ◽

Density Matrix ◽

Finite Temperature ◽

Approximation Scheme ◽

Black Hole Thermodynamics ◽

Extremal Black Hole ◽

Strongly Coupled ◽

Large N

We develop an approximation scheme for the quantum mechanics of N D0-branes at finite temperature in the 't Hooft large-N limit. The entropy of the quantum mechanics calculated using this approximation agrees well with the Bekenstein-Hawking entropy of a ten-dimensional non-extremal black hole with 0-brane charge. This result is in accord with the duality conjectured by Itzhaki, Maldacena, Sonnenschein and Yankielowicz. Our approximation scheme provides a model for the density matrix which describes a black hole in the strongly-coupled quantum mechanics.

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Areas and entropies in BFSS/gravity duality

SciPost Physics ◽

10.21468/scipostphys.8.4.057 ◽

2020 ◽

Vol 8 (4) ◽

Cited By ~ 1

Author(s):

Tarek Anous ◽

Joanna Karczmarek ◽

Eric Mintun ◽

Mark Van Raamsdonk ◽

Benson Way

Keyword(s):

Quantum Mechanics ◽

Gauge Theory ◽

Matrix Model ◽

Finite Temperature ◽

The Matrix ◽

Gravity Duality ◽

General Connection ◽

Ordinary Quantum

The BFSS matrix model provides an example of gauge-theory / gravity duality where the gauge theory is a model of ordinary quantum mechanics with no spatial subsystems. If there exists a general connection between areas and entropies in this model similar to the Ryu-Takayanagi formula, the entropies must be more general than the usual subsystem entanglement entropies. In this note, we first investigate the extremal surfaces in the geometries dual to the BFSS model at zero and finite temperature. We describe a method to associate regulated areas to these surfaces and calculate the areas explicitly for a family of surfaces preserving SO(8) symmetry, both at zero and finite temperature. We then discuss possible entropic quantities in the matrix model that could be dual to these regulated areas.

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Extremal correlators and random matrix theory

Journal of High Energy Physics ◽

10.1007/jhep04(2021)214 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Alba Grassi ◽

Zohar Komargodski ◽

Luigi Tizzano

Keyword(s):

Field Theory ◽

Gauge Theory ◽

Matrix Model ◽

Effective Field Theory ◽

Random Matrix ◽

Correlation Functions ◽

Matrix Theory ◽

Effective Field ◽

Random Matrix Model ◽

Large Charge

Abstract We study the correlation functions of Coulomb branch operators of four-dimensional $$ \mathcal{N} $$ N = 2 Superconformal Field Theories (SCFTs). We focus on rank-one theories, such as the SU(2) gauge theory with four fundamental hypermultiplets. “Extremal” correlation functions, involving exactly one anti-chiral operator, are perhaps the simplest nontrivial correlation functions in four-dimensional Quantum Field Theory. We show that the large charge limit of extremal correlators is captured by a “dual” description which is a chiral random matrix model of the Wishart-Laguerre type. This gives an analytic handle on the physics in some particular excited states. In the limit of large random matrices we find the physics of a non-relativistic axion-dilaton effective theory. The random matrix model also admits a ’t Hooft expansion in which the matrix is taken to be large and simultaneously the coupling is taken to zero. This explains why the extremal correlators of SU(2) gauge theory obey a nontrivial double scaling limit in states of large charge. We give an exact solution for the first two orders in the ’t Hooft expansion of the random matrix model and compare with expectations from effective field theory, previous weak coupling results, and we analyze the non-perturbative terms in the strong ’t Hooft coupling limit. Finally, we apply the random matrix theory techniques to study extremal correlators in rank-1 Argyres-Douglas theories. We compare our results with effective field theory and with some available numerical bootstrap bounds.

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