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Exponential Networks and Representations of Quivers

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arxiv 1611.06177 v2 pith:NZNJSOBW submitted 2016-11-18 hep-th math.AGmath.SG

Richard Eager , Sam Alexandre Selmani , Johannes Walcher This is my paper
classification hep-thmath.AGmath.SG
keywords localnetworksstatescurvedescribeexponentialquiversseveral
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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."

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Cited by 3 Pith papers

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  3. BPS Dendroscopy on Local $\mathbb{P}^1\times \mathbb{P}^1$

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