Chern-Simons theory for the noncommutative 3-torus
Operator Algebras
2012-10-30 v1 High Energy Physics - Theory
Abstract
We study the Chern-Simons action, which was defined for noncommutative spaces in general by the author, for the noncommutative 3-torus, the universal C*-algebra generated by 3 unitaries. D. Essouabri, B. Iochum, C. Levy, and A. Sitarz constructed a spectral triple for the noncommutative 3-torus. We compute the Chern-Simons action for this noncommutative space. In connection with this computation we calculate the first coefficient in the loop expansion series of the corresponding Feynman path integral with the Chern-Simons action as Lagrangian. The result is independent of the deformation matrix of the noncommutative 3-torus and always 0.
Cite
@article{arxiv.1204.0411,
title = {Chern-Simons theory for the noncommutative 3-torus},
author = {Oliver Pfante},
journal= {arXiv preprint arXiv:1204.0411},
year = {2012}
}
Comments
16 pages