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      Noncommutative deformation of four dimensional Einstein gravity

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          Abstract

          We construct a model for noncommutative gravity in four dimensions, which reduces to the Einstein-Hilbert action in the commutative limit. Our proposal is based on a gauge formulation of gravity with constraints. While the action is metric independent, the constraints insure that it is not topological. We find that the choice of the gauge group and of the constraints are crucial to recover a correct deformation of standard gravity. Using the Seiberg-Witten map the whole theory is described in terms of the vierbeins and of the Lorentz transformations of its commutative counterpart. We solve explicitly the constraints and exhibit the first order noncommutative corrections to the Einstein-Hilbert action.

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          Author and article information

          Journal
          05 December 2002
          2003-03-14
          Article
          10.1088/0264-9381/20/8/101
          hep-th/0212071
          01e84a29-6e45-4af8-be51-690062f63faa
          History
          Custom metadata
          IFUM-740-FT
          Class.Quant.Grav. 20 (2003) L95-L104
          LaTex, 11 pages, comments added, to appear in Classical and Quantum Gravity
          hep-th

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