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 ensure that it is not topological. We find that the choice of the gauge group and of the constraints is crucial in recovering 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 the constraints explicitly and exhibit the first-order noncommutative corrections to the Einstein-Hilbert action.

Noncommutative deformation of four-dimensional Einstein gravity / M.A. Cardella, D. Zanon. - In: CLASSICAL AND QUANTUM GRAVITY. - ISSN 0264-9381. - 20:8(2003), pp. L95-L103. [10.1088/0264-9381/20/8/101]

Noncommutative deformation of four-dimensional Einstein gravity

M.A. Cardella;D. Zanon
2003

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 ensure that it is not topological. We find that the choice of the gauge group and of the constraints is crucial in recovering 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 the constraints explicitly and exhibit the first-order noncommutative corrections to the Einstein-Hilbert action.
3 dimensions; gauge; supergravity; spaces
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
http://arxiv.org/abs/hep-th/0212071v4
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/785962
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