Seiberg Duality is an Exceptional Mutation

TL;DR

This paper demonstrates that Seiberg duality in gauge theories from D-branes on del Pezzo singularities can be understood as an admissible mutation of strongly exceptional collections, providing a new mathematical perspective on gauge theory equivalences.

Contribution

It establishes a rigorous mathematical framework linking Seiberg duality to mutations of exceptional collections, advancing the understanding of gauge theory equivalences in string theory.

Findings

Seiberg duality corresponds to mutations of exceptional collections.

The approach provides a consistent mathematical definition of Seiberg duality.

This framework helps classify gauge theories related by duality.

Abstract

The low energy gauge theory living on D-branes probing a del Pezzo singularity of a non-compact Calabi-Yau manifold is not unique. In fact there is a large equivalence class of such gauge theories related by Seiberg duality. As a step toward characterizing this class, we show that Seiberg duality can be defined consistently as an admissible mutation of a strongly exceptional collection of coherent sheaves.