BPS Graphs: From Spectral Networks to BPS Quivers

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.

48 pages, 44 figures

References in corpus (2)

• Webs of five-branes and N=2 superconformal field theories
• Tinkertoys for Gaiotto Duality

Cited by in corpus (15)

• A slow review of the AGT correspondence
• Topological strings, strips and quivers
• Exponential BPS graphs and D brane counting on toric Calabi-Yau threefolds: Part I
• Legendrian Weaves: N-graph Calculus, Flag Moduli and Applications
• Multi-cover skeins, quivers, and 3d $\mathcal{N}=2$ dualities
• On the BPS spectrum of 5d SU(2) super-Yang-Mills
• Line defect Schur indices, Verlinde algebras and $U(1{)}_r$ fixed points
• A geometric recipe for twisted superpotentials
• More on Homological Supersymmetric Quantum Mechanics
• $q$-nonabelianization for line defects
• On the BPS Spectrum of the Rank-1 Minahan-Nemeschansky Theories
• Analysis of world terror networks from the reduced Google matrix of Wikipedia
• An infrared bootstrap of the Schur index with surface defects
• Quantum Line Defects and Refined BPS Spectra
• A note on discrete dynamical systems in theories of class $S$