Some comments on Chern-Simons gauge theory
type: Item
instance of: scholarly article
title: Some comments on Chern-Simons gauge theory
zbMATH Open document ID: 0686.53066
DOI: 10.1007/BF02125132
author: T. R. Ramadas
author: Jonathan Weitsman
author: I. M. Singer
published in: Communications in Mathematical Physics
publication date: 1989-01-01T00:00:00Z
review text: Let M denote a compact 2-manifold without boundary and with genus \(g\geq 3\). With the space \({\mathcal A}\) of connections on the trivial SU(2) bundle on M, there is associated the subspace \({\mathcal A}_ F\) of flat connections and the submanifold \({\mathcal A}^ s_ F\) of irreducible flat connections. The group of gauge transformations is denoted by \({\mathcal G}\); it is well-known that \({\mathcal A}^ s_ F/{\mathcal G}\) is in a natural way a symplectic manifold. The authors show that there exists a natural hermitian line bundle on \({\mathcal A}_ F/{\mathcal G}\). Restricted to \({\mathcal A}^ s_ F/{\mathcal G}\), this line bundle carries a natural connection whose curvature is (up to a factor i) the standard symplectic form. This theorem does not require a choice of conformal structure on M. If M is endowed with a complex structure, this line bundle is isomorphic to the determinant bundle. It is demonstrated how path-integral quantization of the Chern-Simons action yields holomorphic sections of this bundle.
reviewed by: Hanno Rund
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 58D30
Mathematics Subject Classification ID: 81T08
zbMATH DE Number: 4124556
zbMATH Keywords: gauge connections
zbMATH Keywords: hermitian line bundle
zbMATH Keywords: curvature
zbMATH Keywords: complex structure
zbMATH Keywords: Chern-Simons action
Wikidata QID: Q56866910
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02125132
OpenAlex ID: W2004933253
description: scientific article; zbMATH DE number 4124556