Physical phase space of lattice Yang-Mills theory and the moduli space of flat connections on a Riemann surface

Details Physical phase space of lattice Yang-Mills theory and the moduli space of flat connections on a Riemann surface Physical phase space of lattice Yang-Mills theory and the moduli space of flat connections on a Riemann surface

1995-11-03

arxiv.org/abs/hep-th/9511018v1

Theor.Math.Phys.113:1289-1298,1997; Teor.Mat.Fiz.113:100-111,1997

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, latex, no figures

Scientific paper

10.1007/BF02634016

It is shown that the physical phase space of $\g$-deformed Hamiltonian lattice Yang-Mills theory, which was recently proposed in refs.[1,2], coincides as a Poisson manifold with the moduli space of flat connections on a Riemann surface with $(L-V+1)$ handles and therefore with the physical phase space of the corresponding $(2+1)$-dimensional Chern-Simons model, where $L$ and $V$ are correspondingly a total number of links and vertices of the lattice. The deformation parameter $\g$ is identified with $\frac {2\pi}{k}$ and $k$ is an integer entering the Chern-Simons action.

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