Quenched free energy from spacetime D-branes

TL;DR

The paper introduces a new integral representation for quenched free energy applicable to random systems, linking it to spacetime D-branes in gravity, and demonstrates its use in matrix models with expected thermodynamic behavior.

Contribution

It provides a novel integral formula for quenched free energy involving multi-boundary correlators and connects it to spacetime D-branes in gravity theories.

Findings

Quenched free energy decreases monotonically with temperature.

The formalism applies to the Airy limit of random matrix models.

The approach bridges random systems and spacetime D-branes in gravity.

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.