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.
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Okuyama, K., Sakai, K. Resurgence analysis of 2d Yang-Mills theory on a torus. J. High Energ. Phys. 2018, 65 (2018). https://doi.org/10.1007/JHEP08(2018)065
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DOI: https://doi.org/10.1007/JHEP08(2018)065