U(2,2) gravity on noncommutative space with symplectic structure

Details U(2,2) gravity on noncommutative space with symplectic structure U(2,2) gravity on noncommutative space with symplectic structure

2010-06-21

arxiv.org/abs/1006.4074v4

Phys.Rev.D83:024023,2011

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, no figures; v2: 14 pages, clarifications and references added; v3: 16 pages, title changed, clarifications and refer

Scientific paper

10.1103/PhysRevD.83.024023

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.

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