Exponential networks and representations of quivers. (English) Zbl 1381.81096
Summary: 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”.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 14J32 | Calabi-Yau manifolds (algebro-geometric aspects) |
| 32Q25 | Calabi-Yau theory (complex-analytic aspects) |
| 81T60 | Supersymmetric field theories in quantum mechanics |
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