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2012

Extended gravity from noncommutativity

Aschieri, Paolo

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We review the first order theory of gravity (vierbein formulation) on noncommutative spacetime studied in [1, 2].

The first order formalism allows to couple the theory to fermions.
This NC action is then reinterpreted (using the Seiberg-Witten map) as a gravity theory on commutative spacetime that contains terms with higher derivatives and higher powers of the curvature and depend on the noncommutativity parameter \theta.
When the noncommutativity is switched off we recover the usual gravity action coupled to fermions.

Extended gravity from noncommutativity · Around

Built on

P. Aschieri and L. Castellani, “Noncommutative gauge fields coupled to noncommutative gravity,” arXiv:1205.1911 [hep-th]
Original
1911
Earlier work this paper cites.
Yu.Manin, Quantum groups and non-commutative geometry
1988
Earlier work this paper cites.
L.D. Faddeev, N.Yu. Reshetikhin, L.A. Takhtajan, Quantization of Lie groups and Lie algebras
1990
Earlier work this paper cites.
A. Connes, “Non-commutative geometry.” Academic Press, San Diego, CA, 1994, 661 p., ISBN 0-12-185860-X
1994
Earlier work this paper cites.

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P. Aschieri and L. Castellani, “Noncommutative gravity coupled to fermions: second order expansion via Seiberg-Witten map,” arXiv:1111.4822 [hep-th]
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P. Aschieri and L. Castellani, “Extended gravity theories from dynamical noncommutativity,” arXiv:1206.4096 [hep-th]
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Cited in the paper.

Then

K. Ulker, B. Yapiskan, “Seiberg-Witten maps to all orders,” Phys. Rev. D77
Original
2008
Later among the works it cites.
P. Aschieri and L. Castellani, “Noncommutative D=4 gravity coupled to fermions,” JHEP 0906
Original
2009
Later among the works it cites.
P. Aschieri, M. Dimitrijevic, P. Kulish, F. Lizzi, J. Wess, “Noncommutative Spacetimes”, Lecture Notes in Physics, vol. 774, Springer 2009
2009
Later among the works it cites.

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