On the Geometry of Matrix Models for N=1*

TL;DR

This paper explores the geometric structure of matrix models linked to N=1 super Yang-Mills theory, revealing a connection between the Riemann surface solutions and the Donagi-Witten spectral curve, and identifying quantum resolvents geometrically.

Contribution

It uncovers a novel geometric relationship between the Riemann surface of matrix models and the Donagi-Witten spectral curve in N=1 super Yang-Mills theory.

Findings

Riemann surface solutions are related to the Donagi-Witten spectral curve

Quantum resolvents are expressed in terms of geometric data

The geometry provides insights into the matrix model structure

Abstract

We investigate the geometry of the matrix model associated with an N=1 super Yang-Mills theory with three adjoint fields, which is a massive deformation of N=4. We study in particular the Riemann surface underlying solutions with arbitrary number of cuts. We show that an interesting geometrical structure emerges where the Riemann surface is related on-shell to the Donagi-Witten spectral curve. We explicitly identify the quantum field theory resolvents in terms of geometrical data on the surface.