Resurgence analysis of 2d Yang-Mills theory on a torus

Abstract

We study the large $N$ 't Hooft expansion of the partition function of 2d $U(N)$ Yang-Mills theory on a torus. We compute the $1/N$ genus expansion of both the chiral and the full partition function of 2d Yang-Mills using the recursion relation found by Kaneko and Zagier with a slight modification. Then we study the large order behavior of this genus expansion, from which we extract the non-perturbative correction using the resurgence relation. It turns out that the genus expansion is not Borel summable and the coefficient of 1-instanton correction, the so-called Stokes parameter, is pure imaginary. We find that the non-perturbative correction obtained from the resurgence is reproduced from a certain analytic continuation of the grand partition function of a system of non-relativistic fermions on a circle. Our analytic continuation is different from that considered in hep-th/0504221.

45 pages; v2: references added; v3: typos corrected

References in corpus (4)

• Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory
• Quantum Entanglement of Baby Universes
• Cargese lectures on string theory with eight supercharges
• Bosonization of non-relativistic fermions on a circle: Tomonaga's problem revisited

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