Higher Cluster Categories and QFT Dualities

TL;DR

This paper introduces a unified mathematical framework using higher cluster categories and quiver mutations to describe dualities in minimally SUSY gauge theories across various dimensions, revealing an infinite family of generalized dualities.

Contribution

It connects advanced mathematical structures like graded quivers and higher Ginzburg algebras to physical dualities, providing a new perspective on gauge theory equivalences.

Findings

Quiver mutations correspond to gauge theory dualities.

Framework applies to theories from 6d to 0d.

Identifies an infinite family of generalized dualities.

Abstract

We present a unified mathematical framework that elegantly describes minimally SUSY gauge theories in even dimension, ranging from $6d$ to $0d$, and their dualities. This approach combines recent developments on graded quiver with potentials, higher Ginzburg algebras and higher cluster categories (also known as $m$-cluster categories). Quiver mutations studied in the context of mathematics precisely correspond to the order $(m+1)$ dualities of the gauge theories. Our work suggests that these equivalences of quiver gauge theories sit inside an infinite family of such generalized dualities, whose physical interpretation is yet to be understood.