Wall-crossing, open BPS counting and matrix models

Details Wall-crossing, open BPS counting and matrix models Wall-crossing, open BPS counting and matrix models

2010-11-24

arxiv.org/abs/1011.5269v2

JHEP 1103:089,2011; JHEP 1104:046,2011

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, 8 figures, published version

Scientific paper

10.1007/JHEP03(2011)089 10.1007/

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.

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