ADE Spectral Networks and Decoupling Limits of Surface Defects

TL;DR

This paper investigates the vacua and BPS spectra of surface defects in class S theories using ADE spectral networks, revealing new spectra and connections to known 2d models in specific decoupling limits.

Contribution

It introduces a detailed analysis of vacua and BPS spectra of surface defects in decoupling limits, identifying connections to known 2d theories and discovering new spectral phenomena.

Findings

Suppressed 2d-4d BPS mixing in certain IR regions.

Identification of surface defect theories with known 2d models.

Discovery of new vacua and BPS spectra in specific decoupling limits.

Abstract

We study vacua and BPS spectra of canonical surface defects of class $\mathcal{S}$ theories in different decoupling limits using ADE spectral networks. In some regions of the IR moduli spaces of these 2d-4d systems, the mixing between 2d and 4d BPS states is suppressed, and the spectrum of 2d-4d BPS states becomes that of a 2d $\mathcal{N}=(2,2)$ theory. For some decoupling limits, we identify the 2d theories describing the surface defects with nonlinear sigma models and coset models that have been previously studied. We also study certain cases where the decoupling limit of a surface defect exhibits a set of vacua and a BPS spectrum that appear to be entirely new. A detailed analysis of these spectra and their wall-crossing behavior is performed.