On Equivalence of two Hurwitz Matrix Models

TL;DR

This paper explores the equivalence of two matrix models related to Hurwitz partition functions, demonstrating how a Fourier-Laplace transform connects different formulations and deepening understanding of their mathematical structure.

Contribution

It shows the equivalence of two Hurwitz matrix models and introduces a transform linking their representations, advancing the theoretical understanding of these models.

Findings

Fourier-Laplace transform relates two matrix model formulations

Demonstrates equivalence of different Hurwitz matrix models

Provides insights into the structure of Hurwitz partition functions

Abstract

In arXiv:0902.2627 a matrix model representation was found for the simplest Hurwitz partition function, which has Lambert curve phi e^{-phi} = psi as a classical equation of motion. We demonstrate that Fourier-Laplace transform in the logarithm of external field Psi converts it into a more sophisticated form, recently suggested in arXiv:0906.1206.