Two-Dimensional Yang-Mills Theory and Moduli Spaces of Holomorphic Differentials

Details Two-Dimensional Yang-Mills Theory and Moduli Spaces of Holomorphic Differentials Two-Dimensional Yang-Mills Theory and Moduli Spaces of Holomorphic Differentials

2004-08-06

arxiv.org/abs/hep-th/0408055v2

Phys.Lett. B600 (2004) 275-286

Physics

High Energy Physics

High Energy Physics - Theory

14 pages; v2: references added

Scientific paper

10.1016/j.physletb.2004.09.010

We describe and solve a double scaling limit of large N Yang-Mills theory on a two-dimensional torus. We find the exact strong-coupling expansion in this limit and describe its relation to the conventional Gross-Taylor series. The limit retains only the chiral sector of the full gauge theory and the coefficients of the expansion determine the asymptotic Hurwitz numbers, in the limit of infinite winding number, for simple branched coverings of a torus. These numbers are computed exactly from the gauge theory vacuum amplitude and shown to coincide with the volumes of the principal moduli spaces of holomorphic differentials. The string theory interpretation of the double scaling limit is also described.

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