Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models

TL;DR

This paper provides an exact, factorized solution for strongly-coupled single-trace matrix models, extending known integrals and proposing a general orbifold-like method applicable to various models.

Contribution

It introduces a novel exact solution for these matrix models, generalizes classical integrals, and offers a new orbifold-inspired approach for analyzing one-matrix models.

Findings

Exact partition function expressions in closed form

Generalization of Selberg and Kadell integrals

Conjectured correlator formulas for Schur functions

Abstract

We find an exact solution to strongly-coupled matrix models with a single-trace monomial potential. Our solution yields closed form expressions for the partition function as well as averages of Schur functions. The results are fully factorized into a product of terms linear in the rank of the matrix and the parameters of the model. We extend our formulas to include both logarthmic and finite-difference deformations, thereby generalizing the celebrated Selberg and Kadell integrals. We conjecture a formula for correlators of two Schur functions in these models, and explain how our results follow from a general orbifold-like procedure that can be applied to any one-matrix model with a single-trace potential.