U(2,2) gravity on noncommutative space with symplectic structure
Abstract
The classical Einstein's gravity can be reformulated from the constrained U(2,2) gauge theory on the ordinary (commutative) four-dimensional spacetime. Here we consider a noncommutative manifold with a symplectic structure and construct a U(2,2) gauge theory on such a manifold by using the covariant coordinate method. Then we use the Seiberg-Witten map to express noncommutative quantities in terms of their commutative counterparts up to the first-order in noncommutative parameters. After imposing constraints we obtain a noncommutative gravity theory described by the Lagrangian with up to nonvanishing first order corrections in noncommutative parameters. This result coincides with our previous one obtained for the noncommutative SL(2,C) gravity.
Cite
@article{arxiv.1006.4074,
title = {U(2,2) gravity on noncommutative space with symplectic structure},
author = {Yan-Gang Miao and Zhao Xue and Shao-Jun Zhang},
journal= {arXiv preprint arXiv:1006.4074},
year = {2011}
}
Comments
13 pages, no figures; v2: 14 pages, clarifications and references added; v3: 16 pages, title changed, clarifications and references added; v4: 17 pages, clarifications added, this final version accepted by Physical Review D