Exponential BPS graphs and D brane counting on toric Calabi-Yau threefolds: Part I

Abstract

We study BPS spectra of D-branes on local Calabi-Yau threefolds $\mathcal{O}(-p)\oplus \mathcal{O}(p-2)\to {\mathbb{P}}^1$ with $p=0,1$, corresponding to ${\mathbb{C}}^3/{\mathbb{Z}}_2$ and the resolved conifold. Nonabelianization for exponential networks is applied to compute directly unframed BPS indices counting states with D2 and D0 brane charges. Known results on these BPS spectra are correctly reproduced by computing new types of BPS invariants of 3d-5d BPS states, encoded by nonabelianization, through their wall-crossing. We also develop the notion of exponential BPS graphs for the simplest toric examples, and show that they encode both the quiver and the potential associated to the Calabi-Yau via geometric engineering.

52+4 pages

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Cited by in corpus (10)

• Peacock patterns and new integer invariants in topological string theory
• Exact WKB methods in $SU(2)$ $N_f=1$
• Exponential BPS graphs and D brane counting on toric Calabi-Yau threefolds: Part I
• Mathematical structures of non-perturbative topological string theory: from GW to DT invariants
• Exponential Networks, WKB and Topological String
• On the BPS spectrum of 5d SU(2) super-Yang-Mills
• 5D BPS Quivers and KK Towers
• A-branes, foliations and localization
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• Attractor invariants, brane tilings and crystals