Mapping class group actions in Chern-Simons theory with gauge group G ⋉ g*

C. Meusburger, B. J. Schroers

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

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 ? 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. © 2004 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)569-597
Number of pages29
JournalNuclear Physics B
Volume706
Issue number3
DOIs
Publication statusPublished - 7 Feb 2005

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