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

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

2005-05-16

arxiv.org/abs/hep-th/0505143v1

Nucl.Phys. B738 (2006) 425-456

Physics

High Energy Physics

High Energy Physics - Theory

35 pages, 3 eps figures

Scientific paper

10.1016/j.nuclphysb.2006.01.014

We explicitly determine the symplectic structure on the phase space of Chern-Simons theory with gauge group $G\ltimes g^*$ 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 $G\ltimes g^*$. The $(n+1)$st puncture plays a distinguished role and the associated variables lie in the cotangent bundle of $G\ltimes g^*$. 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.

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