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

Abstract

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.

12 pages, latex, no figures

References in corpus (7)

• Symplectic structures associated to Lie-Poisson groups
• Symplectic structure of the moduli space of flat connections on a Riemann surface
• Two dimensional lattice gauge theory based on a quantum group
• Integrability in Hamiltonian Chern-Simons theory
• q-deformed lattice gauge theory and 3-manifold invariants
• Gauge-invariant Hamiltonian formulation of lattice Yang-Mills theory and the Heisenberg double
• An involution and dynamics for the $q$-deformed quantum top

Cited by in corpus (1)

• On a self-dual phase space for 3+1 lattice Yang-Mills theory