Abstract
We define “BPS graphs” on punctured Riemann surfaces associated with A N −1 theories of class \( \mathcal{S} \). 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.
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Gabella, M., Longhi, P., Park, C.Y. et al. BPS graphs: from spectral networks to BPS quivers. J. High Energ. Phys. 2017, 32 (2017). https://doi.org/10.1007/JHEP07(2017)032
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DOI: https://doi.org/10.1007/JHEP07(2017)032