Article ID Journal Published Year Pages File Type
1844398 Nuclear Physics B 2006 32 Pages PDF
Abstract
We explicitly determine the symplectic structure on the phase space of Chern-Simons theory with gauge group G⋉g∗ on a three-manifold of topology R×Sg,n∞, where Sg,n∞ 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∗. The (n+1)st puncture plays a distinguished role and the associated variables lie in the cotangent bundle of G⋉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.
Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
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