The BPS Spectrum Generator In 2d-4d Systems

TL;DR

This paper derives general spectrum generating functions for coupled 2d-4d systems of class S, incorporating surface and line defects, and reproduces known BPS spectra as a validation of the approach.

Contribution

It provides the most general spectrum generating functions for coupled 2d-4d theories of class S with defects, extending previous methods.

Findings

Reproduces well-known BPS spectra

Derives general spectrum generating functions for 2d-4d systems

Applicable to a broad class of coupled systems

Abstract

We apply the techniques provided by the recent works Gaiotto, Moore and Neitzke, to derive the most general spectrum generating functions for coupled 2d-4d $A_1$ theories of class ${\cal S}$, in presence of surface and line defects. As an application of the result, some well-known BPS spectra are reproduced. Our results apply to a large class of coupled 2d-4d systems, the corresponding spectrum generating functions can be easily derived from our general expressions.