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Journal Article

#### Wall Crossing As Seen By Matrix Models

##### Locator

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##### Fulltext (public)

1005.1293

(Preprint), 528KB

CMP307_429.pdf

(Publisher version), 635KB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Ooguri, H., Sułkowski, P., & Yamazaki, M. (2011). Wall Crossing As Seen By Matrix
Models.* Communications in Mathematical Physics,* *307*(2),
429 -462. doi:10.1007/s00220-011-1330-x.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0012-BD1F-7

##### 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 K\"ahler moduli space ${\cal M}(X)$. 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 K\"ahler moduli space ${\cal M}(Y)$
contains two copies of ${\cal M}(X)$, one related to the BPS charges and
another to the stability conditions. The two sets of data are unified in ${\cal
M}(Y)$. 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 $Y$.