We review the role of Drinfeld doubles and κ-Poincaré symmetries in quantised (2+1)gravity and Chern-Simons theory. We discuss the conditions under which a given Hopf algebra symmetry is compatible with a Chern-Simons theory and determine this compatibility explicitly for the Drinfeld doubles and κ-Poincaré symmetries associated with the isometry groups of (2+1)-gravity. In particular, we expla...

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 var...

In [46], Witten related topological string theory on the cotangent bundle T M of a three manifold M to the Chern–Simons gauge theory on M . Gopakumar and Vafa [11] related the topological string theory on the deformed conifold (the cotangent bundle T S of the 3–sphere) to that on the resolved conifold (the total space of OP1. 1/ ̊OP1. 1/! P ). These works lead to a duality between the topologica...

Self-dual vortex solutions are studied in detail in the generalized abelian Higgs model with independent Chern-Simons interaction. For special choices of couplings, it reduces to a Maxwell-Higgs model with two scalar fields, a Chern-Simons-Higgs model with two scalar fields, or other new models. We investigate the properties of the static solutions and perform detailed numerical analyses. For t...

We study dynamics of non-relativistic Chern-Simons solitons, both in the absence and in the presence of external fields. We find that a phase, related to the 1-cocyle of the Galileo group, must be included to give the correct dy-namical behavior. We show that interactions among Chern-Simons solitons are mediated by an effective Chern-Simons gauge field induced by the soli-tons. In the two solit...

In this paper, we prove the existence of finite-energy electrically and magnetically charged vortex solutions in the full Chern–Simons–Higgs theory, for which both the Maxwell term and the Chern–Simons term are present in the Lagrangian density. We consider both Abelian and non-Abelian cases. The solutions are smooth and satisfy natural boundary conditions. Existence is established via a constr...

We work out the relation between Chern-Simons, 2d Yang-Mills on the cylinder, and Brownian motion. We show that for the unitary, orthogonal and symplectic groups, various observables in Chern-Simons theory on S3 and lens spaces are exactly given by counting the number of paths of a Brownian particle wandering in the fundamental Weyl chamber of the corresponding Lie algebra. We construct a fermi...