Wall Crossing As Seen By Matrix Models

Abstract

The number of BPS bound states of D-branes on a Calabi-Yau manifold depends on two sets of data, the BPS charges and the stability conditions. For D0 and D2-branes bound to a single D6-brane wrapping a Calabi-Yau 3-fold X, both are naturally related to the Kahler moduli space M(X). We construct unitary one-matrix models which count such BPS states for a class of toric Calabi-Yau manifolds at infinite 't Hooft coupling. The matrix model for the BPS counting on X turns out to give the topological string partition function for another Calabi-Yau manifold Y, whose Kahler moduli space M(Y) contains two copies of M(X), one related to the BPS charges and another to the stability conditions. The two sets of data are unified in M(Y). The matrix models have a number of other interesting features. They compute spectral curves and mirror maps relevant to the remodeling conjecture. For finite 't Hooft coupling they give rise to yet more general geometry \widetilde{Y} containing Y.

44 pages, 9 figures, published version

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• Unitary Chern-Simons matrix model and the Villain lattice action
• Oscillatory matrix model in Chern-Simons theory and Jacobi-theta determinantal point process
• The remodeling conjecture and the Faber-Pandharipande formula
• The Origin of Calabi-Yau Crystals in BPS States Counting
• A note on statistical model for BPS D4-D2-D0 states
• Charging solid partitions
• Matrix models and stochastic growth in Donaldson-Thomas theory
• Algorithms for representations of quiver Yangian algebras
• Generalized Ablowitz-Ladik hierarchy in topological string theory
• Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues
• Topological String Partition Function on Generalised Conifolds
• GW/DT invariants and 5D BPS indices for strips from topological recursion