BPS Graphs: From Spectral Networks to BPS Quivers

Authors: Maxime Gabella, Pietro Longhi, Chan Y. Park and Masahito Yamazaki Preprint number: UUITP-11/17  We define “BPS graphs” on punctured Riemann surfaces associated with A_{N−1} theories of class S. BPS graphs provide a bridge between two powerful frameworks for studying the spectrum of BPS states: spectral networks and BPS quivers. They arise from degenerate spectral networks at maximal intersections of walls of marginal stability on the Coulomb branch. While the BPS spectrum is ill-defined at such intersections, a BPS graph captures a useful basis of elementary BPS states. The topology of a BPS graph encodes a BPS quiver, even for higher-rank theories and for theories with certain partial punctures. BPS graphs lead to a geometric realization of the combinatorics of Fock-Goncharov N-triangulations and generalize them in several ways.