Wall-crossing, open BPS counting and matrix models
arXiv:1011.5269 · doi:10.1007/JHEP03(2011)089 10.1007/JHEP04(2011)046
Abstract
We consider wall-crossing phenomena associated to the counting of D2-branes attached to D4-branes wrapping lagrangian cycles in Calabi-Yau manifolds, both from M-theory and matrix model perspective. Firstly, from M-theory viewpoint, we review that open BPS generating functions in various chambers are given by a restriction of the modulus square of the open topological string partition functions. Secondly, we show that these BPS generating functions can be identified with integrands of matrix models, which naturally arise in the free fermion formulation of corresponding crystal models. A parameter specifying a choice of an open BPS chamber has a natural, geometric interpretation in the crystal model. These results extend previously known relations between open topological string amplitudes and matrix models to include chamber dependence.
25 pages, 8 figures, published version
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Cited by in corpus (7)
- Wall-Crossing in Coupled 2d-4d Systems
- A slow review of the AGT correspondence
- q-deformations of two-dimensional Yang-Mills theory: Classification, categorification and refinement
- Refined matrix models from BPS counting
- Quiver Yangians and Crystal Melting: A Concise Summary
- A note on statistical model for BPS D4-D2-D0 states
- BPS states, crystals and matrices