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2012

Extended gravity theories from dynamical noncommutativity

Aschieri, Paolo, Castellani, Leonardo

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In this paper we couple noncommutative (NC) vielbein gravity to scalar fields.

Noncommutativity is encoded in a star product between forms, given by an abelian twist (a twist with commuting vector fields).
A geometric generalization of the Seiberg-Witten map for abelian twists yields an extended theory of gravity coupled to scalars, where all fields are ordinary (commutative) fields.
The vectors defining the twist can be related to the scalar fields and their derivatives, and hence acquire dynamics.

Extended gravity theories from dynamical 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.
J. E. Moyal, Quantum mechanics as a statistical theory
1946
Earlier work this paper cites.
N. Seiberg and E. Witten, String theory and noncommutative geometry
1999
Earlier work this paper cites.

Similar

P. Aschieri, M. Dimitrijevic, F. Meyer and J. Wess, “Noncommutative geometry and gravity,” Class. Quant. Grav. 23
2006
Cited alongside, same era.
P. Aschieri, L. Castellani and M. Dimitrijevic, “Dynamical noncommutativity and Noether theorem in twisted ϕ ⋆ 4 \phi^{\star 4} theory,” Lett. Math. Phys. 85
Original
2008
Cited alongside, same era.
P. Aschieri and L. Castellani, “Noncommutative D=4 gravity coupled to fermions,” JHEP 0906
Original
2009
Cited alongside, same era.
P. Aschieri, L. Castellani and M. Dimitrijevic, “Noncommutative gravity at second order via Seiberg-Witten map,” arXiv:1207.4346 [hep-th]
Original
Cited in the paper.

Then

T. Ohl and A. Schenkel, “Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes,” Gen. Rel. Grav. 42
Original
2010
Later among the works it cites.
A. Schenkel and C. F. Uhlemann, “Field Theory on Curved Noncommutative Spacetimes,” SIGMA 6
Original
2010
Later among the works it cites.
P. Aschieri and L. Castellani, “Noncommutative gravity coupled to fermions: second order expansion via Seiberg-Witten map,” JHEP 1207
Original
2012
Closest in time.

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