An invariant action for noncommutative gravity in four dimensions
Abstract
Two main problems face the construction of noncommutative actions for gravity with star products: the complex metric and finding an invariant measure. The only gauge groups that could be used with star products are the unitary groups. I propose an invariant gravitational action in D=4 dimensions based on the constrained gauge group U(2,2) broken to U(1,1)×U(1,1). No metric is used, thus giving a naturally invariant measure. This action is generalized to the noncommutative case by replacing ordinary products with star products. The fourdimensional noncommutative action is studied and the deformed action to first order in deformation parameter is computed.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 June 2003
 DOI:
 10.1063/1.1572199
 arXiv:
 arXiv:hepth/0202137
 Bibcode:
 2003JMP....44.2534C
 Keywords:

 04.90.+e;
 11.30.Ly;
 Other topics in general relativity and gravitation;
 Other internal and higher symmetries;
 High Energy Physics  Theory
 EPrint:
 11 pages. Paper shortened. Consideration is now limited to gravity in fourdimensions