Exponential Networks and Representations of Quivers

Abstract

We study the geometric description of BPS states in supersymmetric theories with eight supercharges in terms of geodesic networks on suitable spectral curves. We lift and extend several constructions of Gaiotto-Moore-Neitzke from gauge theory to local Calabi-Yau threefolds and related models. The differential is multi-valued on the covering curve and features a new type of logarithmic singularity in order to account for D0-branes and non-compact D4-branes, respectively. We describe local rules for the three-way junctions of BPS trajectories relative to a particular framing of the curve. We reproduce BPS quivers of local geometries and illustrate the wall-crossing of finite-mass bound states in several new examples. We describe first steps toward understanding the spectrum of framed BPS states in terms of such "exponential networks."

82 pages, 60 figures, typos fixed

References in corpus (6)

• Elliptic genera of 2d N=2 gauge theories
• Remodeling the B-model
• Witten Index and Wall Crossing
• Exact Results in Supersymmetric Field Theories on Manifolds with Boundaries
• Categorical Tinkertoys for N=2 Gauge Theories
• Spectral Networks with Spin

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• Gauge/Bethe correspondence from quiver BPS algebras
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• On the BPS spectrum of 5d SU(2) super-Yang-Mills
• Holomorphic field theories and Calabi--Yau algebras
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• Why Is Landau-Ginzburg Link Cohomology Equivalent To Khovanov Homology?
• Wall-Crossing Effects on Quiver BPS Algebras
• An infrared bootstrap of the Schur index with surface defects
• Quantum Line Defects and Refined BPS Spectra
• Attractor invariants, brane tilings and crystals
• Exponential Networks for Linear Partitions
• Symplectic cuts and open/closed strings I
• GW/DT invariants and 5D BPS indices for strips from topological recursion
• Les Houches lectures on non-perturbative Seiberg-Witten geometry
• Quantum Curve for strip geometries, Topological Recursion and open GW/DT invariants