Mapping class group actions in Chern-Simons theory with gauge group G ⋉ g*
Meusburger C, Schroers B (2005)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2005
Journal
Publisher: Elsevier
Book Volume: 706
Pages Range: 569-597
Journal Issue: 3
DOI: 10.1016/j.nuclphysb.2004.10.057
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.
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APA:
Meusburger, C., & Schroers, B. (2005). Mapping class group actions in Chern-Simons theory with gauge group G ⋉ g*. Nuclear Physics B, 706(3), 569-597. https://doi.org/10.1016/j.nuclphysb.2004.10.057
MLA:
Meusburger, Cathérine, and Bernd Schroers. "Mapping class group actions in Chern-Simons theory with gauge group G ⋉ g*." Nuclear Physics B 706.3 (2005): 569-597.
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