Quenched free energy from spacetime D-branes

Abstract We propose a useful integral representation of the quenched free energy which is applicable to any random systems. Our formula involves the generating function of multi-boundary correlators, which can be interpreted on the bulk gravity side as spacetime D-branes introduced by Marolf and Maxfield in [arXiv:2002.08950]. As an example, we apply our formalism to the Airy limit of the random matrix model and compute its quenched free energy under certain approximations of the generating function of correlators. It turns out that the resulting quenched free energy is a monotonically decreasing function of the temperature, as expected.

Download Full-text

DISTRIBUTION FUNCTION FOR SHOT NOISE IN WIGNER-DYSON ENSEMBLES

International Journal of Modern Physics B ◽

10.1142/s0217979296000908 ◽

1996 ◽

Vol 10 (16) ◽

pp. 1999-2006 ◽

Cited By ~ 4

Author(s):

K.A. MUTTALIB ◽

Y. CHEN

Keyword(s):

Distribution Function ◽

Generating Function ◽

Matrix Model ◽

Shot Noise ◽

Random Matrix ◽

Zero Temperature ◽

Channel System ◽

Quantum Regime ◽

Random Matrix Model ◽

General Method

We obtain the generating function for shot noise through a random multi-channel system in the zero temperature quantum regime using a random matrix model. The generating function is a product statistic as opposed to a linear one, and we develop a general method to obtain fluctuation properties of such product statistics within a random matrix framework.

Download Full-text

Quenched free energy in random matrix model

Journal of High Energy Physics ◽

10.1007/jhep12(2020)080 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Kazumi Okuyama

Keyword(s):

Free Energy ◽

High Temperature ◽

Matrix Model ◽

Random Matrix ◽

Monotonic Function ◽

Zero Temperature ◽

Random Matrix Model ◽

Replica Trick ◽

Matrix Integral ◽

The Matrix

Abstract We compute the quenched free energy in the Gaussian random matrix model by directly evaluating the matrix integral without using the replica trick. We find that the quenched free energy is a monotonic function of the temperature and the entropy approaches log N at high temperature and vanishes at zero temperature.

Download Full-text

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.

Download Full-text