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 ∗ on a three-manifold of topology R × S g , n ∞ , where S g , 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.