Spectral Networks and Snakes

Understand

We apply and illustrate the techniques of spectral networks in a large collection of A_{K-1} theories of class S, which we call "lifted A_1 theories." Our construction makes contact with Fock and Goncharov's work on higher Teichmuller theory.

• In particular we show that the Darboux coordinates on moduli spaces of flat connections which come from certain special spectral networks coincide with the Fock-Goncharov coordinates.
• We show, moreover, how these techniques can be used to study the BPS spectra of lifted A_1 theories.
• In particular, we determine the spectrum generators for all the lifts of a simple superconformal field theory.