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A Note on q-Deformed Two-Dimensional Yang-Mills and Open Topological Strings

Peng Zhang
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Abstract

In this note we make a test of the open topological string version of the OSV conjecture, proposed in hep-th/0504054, in the toric Calabi-Yau manifold $X= O(-3)\to\mathbf{P}^2$ with background D4-branes wrapped on Lagrangian submanifolds. The D-brane partition function reduces to an expectation value of some inserted operators of a q-deformed Yang-Mills theory living on a chain of $\mathbf{P}^1$'s in the base $\mathbf{P}^2$ of $X$. At large $N$ this partition function can be written as a sum over squares of chiral blocks, which are related to the open topological string amplitudes in the local $\mathbf{P}^2$ geometry with branes at both the outer and inner edges of the toric diagram. This is in agreement with the conjecture.

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Peng Zhang. 2006-11-10. A Note on q-Deformed Two-Dimensional Yang-Mills and Open Topological Strings. https://doi.org/10.1088/0253-6102%2F54%2F2%2F22

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