New Perspectives on Yang-Mills Theories With Sixteen Supersymmetries

TL;DR

This paper develops matrix models for Yang-Mills theories with sixteen supersymmetries across multiple dimensions, revealing deep connections between gauge theory moduli spaces, string theories, and dualities.

Contribution

It introduces new matrix descriptions of supersymmetric Yang-Mills theories in 2 to 5 dimensions, linking gauge theory moduli spaces to string theory frameworks and demonstrating S-duality in the matrix model.

Findings

Matrix models for 2-5 dimensional Yang-Mills theories with 16 supersymmetries.

Equivalence between Coulomb branches and instanton moduli spaces on T^4.

Manifest S-duality in the 4D Yang-Mills matrix model.

Abstract

We describe various approaches that give matrix descriptions of compactified NS five-branes. As a result, we obtain matrix models for Yang-Mills theories with sixteen supersymmetries in dimensions $2,3,4$ and 5. The equivalence of the various approaches relates the Coulomb branch of certain gauge theories to the moduli space of instantons on $T^4$. We also obtain an equivalence between certain six-dimensional string theories. Further, we discuss how various perturbative and non-perturbative features of these Yang-Mills theories appear in their matrix formulations. The matrix model for four-dimensional Yang-Mills is manifestly S-dual. In this case, we describe how electric fluxes, magnetic fluxes and the interaction between vector particles are realized in the matrix model.