Noncommutative Self-dual Gravity

Abstract

Starting from a self-dual formulation of gravity, we obtain a noncommutative theory of pure Einstein theory in four dimensions. In order to do that, we use Seiberg-Witten map. It is shown that the noncommutative torsion constraint is solved by the vanishing of commutative torsion. Finally, the noncommutative corrections to the action are computed up to second order.

15+1 pages, LaTeX, no figures

References in corpus (15)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Quantum Gravity: a Progress Report
• The Standard Model on Non-Commutative Space-Time
• Deformation Quantization: Quantum Mechanics Lives and Works in Phase-Space
• An Invariant Action for Noncommutative Gravity in Four-Dimensions
• Noncommutative deformation of four dimensional Einstein gravity
• Noncommutative Gravity in two Dimensions
• Noncommutative Topological Theories of Gravity
• Why Does Inflation Start at the Top of the Hill?
• Gravitational fields on a noncommutative space
• Noncommutative Einstein-AdS Gravity in three Dimensions
• Gravity on Noncommutative D-Branes
• Noncommutative gravity: fuzzy sphere and others
• Teleparallel Complex Gravity as Foundation for Noncommutative Gravity

Cited by in corpus (50)

• Noncommutative Black Holes, The Final Appeal To Quantum Gravity: A Review
• A Gravity Theory on Noncommutative Spaces
• Symmetry, Gravity and Noncommutativity
• Comments on noncommutative gravity
• Noncommutative Gravity
• Towards Noncommutative Quantum Black Holes
• Exact Solutions with Noncommutative Symmetries in Einstein and Gauge Gravity
• Celestial chiral algebras, colour-kinematics duality and integrability
• Noncommutative BTZ Black Hole and Discrete Time
• Quantum noncommutative gravity in two dimensions
• Geodesic equation in $k$-Minkowski spacetime
• From Moyal deformations to chiral higher-spin theories and to celestial algebras
• Deformation Quantization of Nonholonomic Almost Kahler Models and Einstein Gravity
• On Noncommutative Minisuperspace and the Friedmann equations
• Gauge theories on quantum spaces
• Noncommutative minisuperspace, gravity-driven acceleration and kinetic inflation
• Twisted Covariant Noncommutative Self-dual Gravity
• Noncommutivity and Scalar Field Cosmology
• Can noncommutative effects account for the present speed up of the cosmic expansion?
• Effects of deformed phase space on scalar field cosmology
• Noncommutative Einstein-Maxwell pp-waves
• Non Commutative Bianchi type II Quantum Cosmology
• OSp(1|4) supergravity and its noncommutative extension
• WKB Approximation in Noncommutative Gravity
• On some models of geometric noncommutative general relativity
• Seiberg--Witten maps for $\mathbf{SO}(1,3)$ gauge invariance and deformations of gravity
• Field Theory on Curved Noncommutative Spacetimes
• Deformed Phase Space Kaluza-Klein cosmology and late time acceleration
• Noncommutative gauge theory using covariant star product defined between Lie-valued differential forms
• Noncommutativity, Saez-Ballester theory and kinetic inflation
• Uniformly accelerated detector in the $\kappa$-deformed Dirac vacuum
• Noncommutative gravity with self-dual variables
• Scalar field in the Bianchi I: Non commutative classical and Quantum Cosmology
• Noncommutative Effects in the Black Hole Evaporation in Two Dimensions
• WKB-type Approximation to Noncommutative Quantum Cosmology
• On the Entropy of Deformed Phase Space Black Hole and the Cosmological Constant
• Background independent noncommutative gravity from Fedosov quantization of endomorphism bundle
• Self-dual road to noncommutative gravity with twist: a new analysis
• Quantum Entanglement of Fermions- Antifermions Pair Creation modes in Non-commutative Bianchi I Space-time
• Noncommutative Effective LQC: inclusion of potential term
• De Donder-Weyl Hamiltonian formalism of MacDowell-Mansouri gravity
• Gravity in Extreme Regions Based on Noncommutative Quantization of Teleparallel Gravity
• A Noncommutative Deformation of Topological Field Theory
• Noncommutative SUSY Black Holes
• Gravitational Anomalies in Noncommutative Field Theory
• $\mathcal{O}(\theta )$ Feynman rules for quadrilinear gauge boson couplings in noncommutative standard model
• Symmetry breaking in nonuniform noncommutative $\lambda {\varphi }^4$ theory at finite temperature
• Noncommutative Topological Half-flat Gravity
• Gauge theory models on $\kappa$-Minkowski space: Results and prospects
• (Pre)-Inflationary Dynamics with Starobinsky Potential in Noncommutative Effective LQC