BPS Wall Crossing and Topological Strings

Abstract

By embedding N=2 gauge theories in string theory and utilizing string dualities we map the counting of BPS states with arbitrary electric and magnetic charges to computations of an A-model topological string on an associated geometry constructed from the data of the SW curve. We show how the conjecture of Kontsevich and Soibelman regarding wall crossing, as well as a more refined version which captures the spin content of BPS states, is a natural consequence. Chern-Simons theory realized on A-branes and a twistorial construction play key roles.

18 pages, additional references

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Cited by in corpus (31)

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• Spectral networks
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• N=2 Quantum Field Theories and Their BPS Quivers
• Quantum Wall Crossing in N=2 Gauge Theories
• Topological Anti-Topological Fusion in Four-Dimensional Superconformal Field Theories
• On Arnold's 14 `exceptional' N=2 superconformal gauge theories
• Categorical Tinkertoys for N=2 Gauge Theories
• An Index Formula for Supersymmetric Quantum Mechanics
• Open BPS Wall Crossing and M-theory
• Wall Crossing, Quivers and Crystals
• Type II/F-theory Superpotentials with Several Deformations and N=1 Mirror Symmetry
• More Arnold's N = 2 superconformal gauge theories
• Wall-crossing of D4-D2-D0 and flop of the conifold
• Refined Black Hole Ensembles and Topological Strings
• Spectral Networks and Snakes
• 2d Wall-Crossing, R-twisting, and a Supersymmetric Index
• On a hyperholomorphic line bundle over the Coulomb branch
• The BPS spectrum of the 4d N=2 SCFT's H_1, H_2, D_4, E_6, E_7, E_8
• BPS spectrum, wall crossing and quantum dilogarithm identity
• Discrete Integrable Systems, Supersymmetric Quantum Mechanics, and Framed BPS States - I
• Correspondence Theorem between Holomorphic Discs and Tropical Discs on K3 Surfaces
• Wall-crossing holomorphic anomaly and mock modularity of multiple M5-branes
• $Y$ systems, $Q$ systems, and 4D $\mathcal{N}=2$ supersymmetric QFT
• Equivalence of Three Wall Crossing Formulae
• K3 metrics from little string theory
• Matrix models and stochastic growth in Donaldson-Thomas theory
• Four-dimensional N=2 Field Theory and Physical Mathematics
• Tangles, Generalized Reidemeister Moves, and Three-Dimensional Mirror Symmetry
• M5-brane prongs, string soliton bound states and wall-crossing