BPS Quivers and Spectra of Complete N=2 Quantum Field Theories

TL;DR

This paper investigates the BPS spectra of four-dimensional N=2 complete quantum field theories, using geometric methods involving M5 branes and triangulations to determine quivers and spectra, including for asymptotically free and Argyres-Douglas models.

Contribution

It introduces a geometric approach to fix BPS quivers and superpotentials for N=2 theories using triangulations of Riemann surfaces, enabling spectrum determination.

Findings

All studied theories have a chamber with finitely many BPS states.

Explicit spectra are determined for asymptotically free and Argyres-Douglas models.

The method applies to theories defined by punctured spheres and tori.

Abstract

We study the BPS spectra of N=2 complete quantum field theories in four dimensions. For examples that can be described by a pair of M5 branes on a punctured Riemann surface we explain how triangulations of the surface fix a BPS quiver and superpotential for the theory. The BPS spectrum can then be determined by solving the quantum mechanics problem encoded by the quiver. By analyzing the structure of this quantum mechanics we show that all asymptotically free examples, Argyres-Douglas models, and theories defined by punctured spheres and tori have a chamber with finitely many BPS states. In all such cases we determine the spectrum.