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Macdonald’s Identities and the Large N Limit of YM 2 on the Cylinder

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The purpose of this paper is to determine the large N asymptotics of the free energy F N (a,U|A) of YM 2 (two-dimensional Yang Mills theory) with gauge group G N =SU(N) on a cylinder where a is a so-called principal element of type ρ. Mathematically, where H G N is the central heat kernel of G N . We find that where Ξ is an explicit quadratic functional in the limit distribution dΣ of eigenvalues of U N , depending only on the integral geometry of SU(2). The factor of N contradicts some predictions in the physics literature on the large N limit of YM 2 on the cylinder (due to Gross-Matytsin, Kazakov-Wynter, and others).

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Authors and Affiliations

  1. Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, USA

    Steve Zelditch

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  1. Steve Zelditch
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Correspondence to Steve Zelditch.

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Communicated by M. R. Douglas

Research partially supported by NSF grant #DMS-0071358 and by the Clay Mathematics Institute.

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Zelditch, S. Macdonald’s Identities and the Large N Limit of YM 2 on the Cylinder. Commun. Math. Phys. 245, 611–626 (2004). https://doi.org/10.1007/s00220-003-1027-x

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