Holomorphic anomaly of 2d Yang-Mills theory on a torus revisited

Abstract

We study the large $N$ 't Hooft expansion of the chiral partition function of 2d $U(N)$ Yang-Mills theory on a torus. There is a long-standing puzzle that no explicit holomorphic anomaly equation is known for the partition function, although it admits a topological string interpretation. Based on the chiral boson interpretation we clarify how holomorphic anomaly arises and propose a natural anti-holomorphic deformation of the partition function. Our deformed partition function obeys a fairly traditional holomorphic anomaly equation. Moreover, we find a closed analytic expression for the deformed partition function. We also study the behavior of the deformed partition function both in the strong coupling/large area limit and in the weak coupling/small area limit. In particular, we observe that drastic simplification occurs in the weak coupling/small area limit, giving another nontrivial support for our anti-holomorphic deformation.

30 pages, 7 figures, v2: typos corrected, published version

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Cited by in corpus (3)

• The phase diagram of $T\bar{T}$-deformed Yang-Mills theory on the sphere
• Resurgence in 2-dimensional Yang-Mills and a genus altering deformation
• Boson-Fermion Correspondence and Holomorphic Anomaly Equation in 2d Yang-Mills Theory on Torus