N=2 Quantum Field Theories and Their BPS Quivers

TL;DR

This paper investigates the connection between 4D N=2 quantum field theories and their BPS quivers, introducing a mutation-based method to determine BPS spectra across various theories, including super-Yang-Mills and M5-brane models.

Contribution

It develops a novel mutation approach for analyzing BPS spectra in N=2 theories, linking quiver mutations to dualities and moduli space patches.

Findings

Successfully determines BPS spectra for super-Yang-Mills with ADE gauge groups.

Applies the mutation method to M5-brane theories on punctured spheres.

Reveals the role of quiver mutations in understanding dualities and spectrum consistency.

Abstract

We explore the relationship between four-dimensional N=2 quantum field theories and their associated BPS quivers. For a wide class of theories including super-Yang-Mills theories, Argyres-Douglas models, and theories defined by M5-branes on punctured Riemann surfaces, there exists a quiver which implicitly characterizes the field theory. We study various aspects of this correspondence including the quiver interpretation of flavor symmetries, gauging, decoupling limits, and field theory dualities. In general a given quiver describes only a patch of the moduli space of the field theory, and a key role is played by quantum mechanical dualities, encoded by quiver mutations, which relate distinct quivers valid in different patches. Analyzing the consistency conditions imposed on the spectrum by these dualities results in a powerful and novel mutation method for determining the BPS states. We apply our method to determine the BPS spectrum in a wide class of examples, including the strong coupling spectrum of super-Yang-Mills with an ADE gauge group and fundamental matter, and trinion theories defined by M5-branes on spheres with three punctures.