Higher cluster categories and QFT dualities

Abstract

We introduce a unified mathematical framework that elegantly describes minimally supersymmetry gauge theories in even dimensions, ranging from six dimensions to zero dimensions, and their dualities. This approach combines and extends recent developments on graded quivers 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 indicates that these equivalences of quiver gauge theories sit inside an infinite family of such generalized dualities.