Spectral Networks with Spin

Understand

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.