Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-11-05
Nucl.Phys. B547 (1999) 375-396
Physics
High Energy Physics
High Energy Physics - Theory
28 pages, revtex, no figures
Scientific paper
10.1016/S0550-3213(99)00089-9
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.
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