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

Abstract

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.

arXiv comment14 pages; v2: references added

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Cited by in corpus (5)

• Conformal perturbation theory and higher spin entanglement entropy on the torus
• Resurgence analysis of 2d Yang-Mills theory on a torus
• Holomorphic anomaly of 2d Yang-Mills theory on a torus revisited
• Double Scaling String Theory of QCD in Two Dimensions
• Instantons, Fluxons and Open Gauge String Theory