Spectral Networks and Snakes

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.

80 pages, 31 figures

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Cited by in corpus (14)

• Spectral networks
• Central charges and RG flow of strongly-coupled N=2 theory
• Wild Wall Crossing and BPS Giants
• Argyres-Douglas Theories and S-Duality
• New Directions in Bipartite Field Theories
• BPS spectrum of Argyres-Douglas theory via spectral network
• The quiver approach to the BPS spectrum of a 4d N=2 gauge theory
• BPS spectrum, wall crossing and quantum dilogarithm identity
• The BPS Spectrum Generator In 2d-4d Systems
• Confinement and duality in supersymmetric gauge theories
• K3 metrics from little string theory
• Four-dimensional N=2 Field Theory and Physical Mathematics
• BPS spectra from BPS graphs
• Singularity Structure of N=2 Supersymmetric Yang-Mills Theories: A Review