Generalised Chern-Simons actions for 3d gravity and κ-Poincaré symmetry
Meusburger C, Schroers B (2009)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2009
Journal
Publisher: Elsevier
Book Volume: 806
Pages Range: 462-488
Journal Issue: 3
DOI: 10.1016/j.nuclphysb.2008.06.023
Abstract
We consider Chern-Simons theories for the Poincaré, de Sitter and anti-de Sitter groups in three dimensions which generalise the Chern-Simons formulation of 3d gravity. We determine conditions under which κ-Poincaré symmetry and its de Sitter and anti-de Sitter analogues can be associated to these theories as quantised symmetries. Assuming the usual form of those symmetries, with a timelike vector as deformation parameter, we find that such an association is possible only in the de Sitter case, and that the associated Chern-Simons action is not the gravitational one. Although the resulting theory and 3d gravity have the same equations of motion for the gauge field, they are not equivalent, even classically, since they differ in their symplectic structure and the coupling to matter. We deduce that κ-Poincaré symmetry is not associated to either classical or quantum gravity in three dimensions. Starting from the (non-gravitational) Chern-Simons action we explain how to construct a multi-particle model which is invariant under the classical analogue of κ-de Sitter symmetry, and carry out the first steps in that construction. © 2008 Elsevier B.V. All rights reserved.
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APA:
Meusburger, C., & Schroers, B. (2009). Generalised Chern-Simons actions for 3d gravity and κ-Poincaré symmetry. Nuclear Physics B, 806(3), 462-488. https://doi.org/10.1016/j.nuclphysb.2008.06.023
MLA:
Meusburger, Cathérine, and Bernd Schroers. "Generalised Chern-Simons actions for 3d gravity and κ-Poincaré symmetry." Nuclear Physics B 806.3 (2009): 462-488.
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