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

Ambar Sengupta
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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 $dμ_T(ø) =N_T^{-1}e^{-S_{YM}(ø)/T}[{\cal D}ø]$ converge, as $T\downarrow 0$, to integrals with respect to a symplectic volume measure $μ_0$ on the moduli space of flat connections on the bundle. These moduli spaces and the symplectic structures are described explicitly.

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Ambar Sengupta. 1994-02-24. The Semiclassical Limit for $SU(2)$ and $SO(3)$ Gauge Theory on the Torus. https://doi.org/10.1007/bf02099474

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