Spectral Networks with Spin

TL;DR

This paper introduces an extension of spectral networks to compute the spin content of BPS spectra in 4D N=2 theories, linking spin to path writhe on Seiberg-Witten curves and connecting to quiver and Chern-Simons theories.

Contribution

It develops an algorithm to determine the spin of BPS states using spectral networks and identifies spin with the writhe of paths on Seiberg-Witten curves, a novel approach.

Findings

Algorithm for computing BPS spin content

Identification of spin with path writhe

Connections to quiver and Chern-Simons theories

Abstract

The BPS spectrum of d=4 N=2 field theories in general contains not only hyper- and vector-multipelts but also short multiplets of particles with arbitrarily high spin. This paper extends the method of spectral networks to give an algorithm for computing the spin content of the BPS spectrum of d=4 N=2 field theories of class S. The key new ingredient is an identification of the spin of states with the writhe of paths on the Seiberg-Witten curve. Connections to quiver representation theory and to Chern-Simons theory are briefly discussed.