Duality and integrability of supermatrix model with external source

TL;DR

This paper explores the Hermitian supermatrix model with an external source, deriving formulas for its partition function and characteristic polynomial ratios, revealing duality and integrability properties related to Toda lattice equations.

Contribution

It introduces a determinantal formula for the supermatrix partition function and demonstrates the model's duality and integrability features, connecting to Toda lattice equations.

Findings

Derived determinantal formulas for the supermatrix partition function

Established duality between characteristic polynomial and external source

Showed the supermatrix integral satisfies Toda lattice equations

Abstract

We study the Hermitian supermatrix model involving an external source. We derive the determinantal formula for the supermatrix partition function, and also for the expectation value of the characteristic polynomial ratio, which yields the duality between the characteristic polynomial and the external source with an arbitrary matrix potential function. We also show that the supermatrix integral satisfies the one and two dimensional Toda lattice equations as well as the ordinary matrix model.