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

Abstract

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 $d{\mu }_T(ø)=N_T^{-1}{e}^{-S_{YM}(ø)/T}[\mathcal{D}ø]$ 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.

18 pages

References in corpus (2)

• Two Dimensional Gauge Theories Revisited
• The Semiclassical Limit of the Two Dimensional Quantum Yang-Mills Model

Cited by in corpus (1)

• The Semiclassical Limit of the Two Dimensional Quantum Yang-Mills Model