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 four-dimensional noncommutative action is studied and the deformed action to first order in deformation parameter is computed.
Journal of Mathematical Physics
- Pub Date:
- June 2003
- Other topics in general relativity and gravitation;
- Other internal and higher symmetries;
- High Energy Physics - Theory
- 11 pages. Paper shortened. Consideration is now limited to gravity in four-dimensions