Phase space structure of Chern-Simons theory with a non-standard puncture

Abstract

We explicitly determine the symplectic structure on the phase space of Chern-Simons theory with gauge group $G⋉g^{\ast }$ on a three-manifold of topology $R\times S$, where $S$ is a surface of genus $g$ with $n+1$ punctures. At each puncture additional variables are introduced and coupled minimally to the Chern-Simons gauge field. The first $n$ punctures are treated in the usual way and the additional variables lie on coadjoint orbits of $G⋉g^{\ast }$. The $(n+1)$st puncture plays a distinguished role and the associated variables lie in the cotangent bundle of $G⋉g^{\ast }$. This allows us to impose a curvature singularity for the Chern-Simons gauge field at the distinguished puncture with an arbitrary Lie algebra valued coefficient. The treatment of the distinguished puncture is motivated by the desire to construct a simple model for an open universe in the Chern-Simons formulation of $(2+1)$-dimensional gravity.

35 pages, 3 eps figures

References in corpus (1)

• Boundary conditions and symplectic structure in the Chern-Simons formulation of (2+1)-dimensional gravity

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