Three dimensional construction of the Virasoro-Bott group

Autor:	Frenkel, Igor B., Kim, Hyun Kyu
Rok vydání:	2021
Předmět:	Mathematics - Geometric Topology High Energy Physics - Theory Mathematical Physics 81R10 17B68 22E65 58D05
Druh dokumentu:	Working Paper
Popis:	We present a three-dimensional geometric construction of the Virasoro-Bott group, which is a central extension of the group of diffeomorphisms of the circle. Our approach is analogous to the well-known construction of a central extension of the loop group by means of the Wess-Zumino topological term. In particular, the Virasoro-Bott group is realized as a quotient group of diffeomorphisms of the disc with special boundary conditions. We identify the Lie algebra corresponding to our group with the Virasoro algebra. We also show that for generalized boundary conditions the Virasoro algebra is extended to a semidirect product with the Heisenberg algebra. We discuss the relation between our construction, the Chern-Simons theory, and the three-dimensional gravity. Comment: 41 pages. v1: The present paper is a preliminary version, and was mostly written by 2014 / v2: minor changes
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2107.11693 Zobrazit plný text záznamu View this record from Arxiv