Supersymmetric gauged matrix models from dimensional reduction on a sphere

TL;DR

This paper demonstrates that a proposed four-fold duality (quadrality) in supersymmetric gauged matrix models can be derived from the two-dimensional Gadde-Gukov-Putrov triality by compactifying on a sphere and analyzing the zero-mode sector.

Contribution

It shows how the zero-dimensional quadrality in supersymmetric gauged matrix models can be inferred from the two-dimensional triality via sphere compactification and R-charge choice.

Findings

Derivation of matrix model quadrality from 2D triality

Connection between sphere compactification and dualities

Extension of triality to full quadrality in matrix models

Abstract

It was recently proposed that N=1 supersymmetric gauged matrix models have a duality of order four - that is, a quadrality - reminiscent of infrared dualities of SQCD theories in higher dimensions. In this note, we show that the zero-dimensional quadrality proposal can be infered from the two-dimensional Gadde-Gukov-Putrov triality. We consider two-dimensional N=(0,2) SQCD compactified on a sphere with the half-topological twist. For a convenient choice of R-charge, the zero-mode sector on the sphere gives rise to a simple N=1 gauged matrix model. Triality on the sphere then implies a triality relation for the supersymmetric matrix model, which can be completed to the full quadrality.