The Semiclassical Limit for $SU(2)$ and $SO(3)$ Gauge Theory on the Torus

Details The Semiclassical Limit for $SU(2)$ and $SO(3)$ Gauge Theory on the Torus The Semiclassical Limit for $SU(2)$ and $SO(3)$ Gauge Theory on the Torus

1994-02-24

arxiv.org/abs/hep-th/9402140v1

Commun.Math.Phys.169:297-314,1995

Physics

High Energy Physics

High Energy Physics - Theory

18 pages

Scientific paper

10.1007/BF02099474

We prove that for $SU(2)$ and $SO(3)$ quantum gauge theory on a torus, holonomy expectation values with respect to the Yang-Mills measure $d\mu_T(\o) =N_T^{-1}e^{-S_{YM}(\o)/T}[{\cal D}\o]$ converge, as $T\downarrow 0$, to integrals with respect to a symplectic volume measure $\mu_0$ on the moduli space of flat connections on the bundle. These moduli spaces and the symplectic structures are described explicitly.

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