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

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.

14 pages, 3 figures

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