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Article
Report number	arXiv:1611.06177
Title	Exponential Networks and Representations of Quivers
Related title	Exponential Networks and Representations of Quivers
Author(s)	Eager, Richard (Heidelberg U.) ; Selmani, Sam Alexandre (Heidelberg U. ; McGill U.) ; Walcher, Johannes (Heidelberg U. ; CERN)
Publication	2017-08-17
Imprint	18 Nov 2016
Number of pages	82
Note	82 pages, 60 figures, typos fixed
In:	JHEP 08 (2017) 063
DOI	10.1007/JHEP08(2017)063
Subject category	math.SG ; Mathematical Physics and Mathematics ; math.AG ; hep-th ; Particle Physics - Theory
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."
Copyright/License	arXiv nonexclusive-distrib. 1.0

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