Spectral Networks and Snakes
Davide Gaiotto, Gregory W. Moore, Andrew Neitzke

TL;DR
This paper explores spectral networks in lifted A_1 theories, connecting them with higher Teichmuller theory and Fock-Goncharov coordinates, and uses these techniques to analyze BPS spectra.
Contribution
It demonstrates how spectral networks relate to Fock-Goncharov coordinates and applies this to study BPS spectra in lifted A_1 theories.
Findings
Darboux coordinates match Fock-Goncharov coordinates
Spectral networks can determine BPS spectra
Spectrum generators are identified for specific theories
Abstract
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.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Nonlinear Waves and Solitons · Algebraic structures and combinatorial models
