The instanton contributions to Yang-Mills theory on the torus: localization, Wilson loops and the perturbative expansion

Abstract

The instanton contributions to the partition function and to homologically trivial Wilson loops for a U(N) Yang-Mills theory on a torus $T^2$ are analyzed. An exact expression for the partition function is obtained as a sum of contributions localized around the classical solutions of Yang-Mills equations, that appear according to the general classification of Atiyah and Bott. Explicit expressions for the exact Wilson loop averages are obtained when N=2, N=3. For general $N$ the contribution of the zero-instanton sector has been carefully derived in the decompactification limit, reproducing the sum of the perturbative series on the plane, in which the light-cone gauge Yang-Mills propagator is prescribed according to Wu-Mandelstam-Leibbrandt (WML). Agreement with the results coming from $S^2$ is therefore obtained, confirming the truly perturbative nature of the WML computations.

28 pages, revtex, no figures

References in corpus (6)

• Matrix String Theory
• Two-dimensional QCD, instanton contributions and the perturbative Wu-Mandelstam-Leibbrandt prescription
• Matrix String Partition Functions
• Two-Dimensional QCD in the Wu-Mandelstam-Leibbrandt Prescription
• Time exponentiation of a Wilson loop for Yang-Mills theories in 2+εdimensions
• Two-dimensional Yang-Mills theory in the leading 1/N expansion revisited

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• Two-Dimensional Yang-Mills Theory and Moduli Spaces of Holomorphic Differentials
• Topological Strings, Two-Dimensional Yang-Mills Theory and Chern-Simons Theory on Torus Bundles
• Double Scaling String Theory of QCD in Two Dimensions
• Instantons, Fluxons and Open Gauge String Theory
• D-Branes in Noncommutative Field Theory
• Wilson Loops in Two-Dimensional Yang-Mills Theories