Quantum double and $\kappa$-Poincar\'e symmetries in (2+1)-gravity and Chern-Simons theory
Abstract
We review the role of Drinfeld doubles and kappa-Poincare symmetries in quantised (2+1)-gravity and Chern-Simons theory. We discuss the conditions under which a given Hopf algebra symmetry is compatible with a Chern-Simons theory and determine this compatibility explicitly for the Drinfeld doubles and kappa-Poincare symmetries associated with the isometry groups of (2+1)-gravity. In particular, we explain that the usual kappa-Poincare symmetries with a timelike deformation are not directly associated with (2+1)-gravity. These kappa-Poincare symmetries are linked to Chern-Simons theory only in the de Sitter case, and the relevant Chern-Simons theory is physically inequivalent to (2+1)-gravity.
Keywords
Cite
@article{arxiv.0809.0052,
title = {Quantum double and $\kappa$-Poincar\'e symmetries in (2+1)-gravity and Chern-Simons theory},
author = {C. Meusburger},
journal= {arXiv preprint arXiv:0809.0052},
year = {2023}
}
Comments
11 pages, no figures, expanded version of talk at the conference Theory Canada 4, references and explanations added, typos corrected