Noncommutative gravity at second order via Seiberg-Witten map

Abstract

We develop a general strategy to express noncommutative actions in terms of commutative ones by using a recently developed geometric generalization of the Seiberg-Witten map (SW map) between noncommutative and commutative fields. We apply this general scheme to the noncommutative vierbein gravity action and provide a SW differential equation for the action itself as well as a recursive solution at all orders in the noncommutativity parameter θ. We thus express the action at order θ^n+2 in terms of noncommutative fields of order at most θ^n+1 and, iterating the procedure, in terms of noncommutative fields of order at most θ^n. This in particular provides the explicit expression of the action at order θ^2 in terms of the usual commutative spin connection and vierbein fields. The result is an extended gravity action on commutative spacetime that is manifestly invariant under local Lorentz rotations and general coordinate transformations.

14 pages

References in corpus (8)

• Extended Theories of Gravity
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Noncommutative D=4 gravity coupled to fermions
• Noncommutative gravity coupled to fermions: second order expansion via Seiberg-Witten map
• Seiberg--Witten Maps to All Orders
• AdS-inspired noncommutative gravity on the Moyal plane
• Noncommutative gauge fields coupled to noncommutative gravity
• Extended gravity theories from dynamical noncommutativity

Cited by in corpus (27)

• Noncommutative Scalar Quasinormal Modes of the Reissner Nordström Black Hole
• Noncommutative Chern-Simons gauge and gravity theories and their geometric Seiberg-Witten map
• Braided $L_{\infty }$-Algebras, Braided Field Theory and Noncommutative Gravity
• Noncommutative SO(2,3) gauge theory and noncommutative gravity
• AdS-inspired noncommutative gravity on the Moyal plane
• OSp(1|4) supergravity and its noncommutative extension
• Microscopic derivation of Dirac composite fermion theory: Aspects of noncommutativity and pairing instabilities
• Photon self-interaction on deformed spacetime
• Noncommutative gravity and the relevance of the $\theta$-constant deformation
• Footprint of spatial noncommutativity in resonant detectors of gravitational wave
• Metric perturbations in Noncommutative Gravity
• Noncommutative gravity with self-dual variables
• Noncommutative gauge and gravity theories and geometric Seiberg-Witten map
• Noncommutative Electrodynamics from $SO(2,3{)}_{\star }$ Model of Noncommutative Gravity
• Background independent noncommutative gravity from Fedosov quantization of endomorphism bundle
• The hybrid Seiberg-Witten map, its $\theta$-exact expansion and the antifield formalism
• Dirac field and gravity in NC $SO(2,3{)}_{\star }$ model
• Photon polarization tensor on deformed spacetime: A four-photon-tadpole contribution
• On almost commutative Friedmann-Lemaître-Robertson-Walker geometries
• Self-dual road to noncommutative gravity with twist: a new analysis
• Noncommutative Reissner-Nordström black hole from noncommutative charged scalar field
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• Canonical Deformation of $N=2$ $Ad{S}_4$ SUGRA
• Seiberg-Witten Map with Lorentz-Invariance and Gauge-Covariant Star Product
• Chern-Simons supergravities, with a twist
• Noncommutative $D=5$ Chern-Simons Gravity: Kaluza-Klein Reduction and Chiral Gravitational Anomaly
• A bigravity model from noncommutative geometry