Mapping class group actions in Chern-Simons theory with gauge group $G\ltimes\mathfrak{g}^*$

Details Mapping class group actions in Chern-Simons theory with gauge group $G\ltimes\mathfrak{g}^*$ Mapping class group actions in Chern-Simons theory with gauge group $G\ltimes\mathfrak{g}^*$

2003-12-04

arxiv.org/abs/hep-th/0312049v2

Nucl.Phys. B706 (2005) 569-597

Physics

High Energy Physics

High Energy Physics - Theory

30 pages, 5 eps figures; corrections concerning the mapping class group which acts on the Poisson algebra discussed in the pap

Scientific paper

10.1016/j.nuclphysb.2004.10.057

We study the action of the mapping class group of an oriented genus g surface with n punctures and a disc removed on a Poisson algebra which arises in the combinatorial description of Chern-Simons gauge theory when the gauge group is a semidirect product $G\ltimes\mathfrak{g}^*$. We prove that the mapping class group acts on this algebra via Poisson isomorphisms and express the action of Dehn twists in terms of an infinitesimally generated G-action. We construct a mapping class group representation on the representation spaces of the associated quantum algebra and show that Dehn twists can be implemented via the ribbon element of the quantum double D(G) and the exchange of punctures via its universal R-matrix.

Affiliated with

Also associated with

No associations

Rating

Mapping class group actions in Chern-Simons theory with gauge group $G\ltimes\mathfrak{g}^*$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Mapping class group actions in Chern-Simons theory with gauge group $G\ltimes\mathfrak{g}^*$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Mapping class group actions in Chern-Simons theory with gauge group $G\ltimes\mathfrak{g}^*$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-630851