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  Wall Crossing As Seen By Matrix Models

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.

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Ooguri, Hirosi1, Author           
Sułkowski, Piotr, Author
Yamazaki, Masahito, Author
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1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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Free keywords: High Energy Physics - Theory, hep-th,Mathematical Physics, math-ph,Mathematics, Algebraic Geometry, math.AG,Mathematics, Mathematical Physics, math.MP
 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 $Y$.

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 Dates: 2010-05-072011
 Publication Status: Issued
 Pages: 43 pages, 9 figures
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 Rev. Type: -
 Identifiers: arXiv: 1005.1293
DOI: 10.1007/s00220-011-1330-x
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Title: Communications in Mathematical Physics
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Publ. Info: Heidelberg : Springer-Verlag Heidelberg
Pages: - Volume / Issue: 307 (2) Sequence Number: - Start / End Page: 429 - 462 Identifier: ISSN: 0010-3616
CoNE: https://pure.mpg.de/cone/journals/resource/954925392313