Noncommutative D=4 gravity coupled to fermions

Abstract

We present a noncommutative extension of Einstein-Hilbert gravity in the context of twist-deformed space-time, with a $\star$-product associated to a quite general triangular Drinfeld twist. In particular the $\star$-product can be chosen to be the usual Groenewald-Moyal product. The action is geometric, invariant under diffeomorphisms and centrally extended Lorentz $\star$-gauge transformations. In the commutative limit it reduces to ordinary gravity, with local Lorentz invariance and usual real vielbein. This we achieve by imposing a charge conjugation condition on the noncommutative vielbein. The theory is coupled to fermions, by adding the analog of the Dirac action in curved space. A noncommutative Majorana condition can be imposed, consistent with the $\star$-gauge transformations. Finally, we discuss the noncommutative version of the Mac-Dowell Mansouri action, quadratic in curvatures.

19 pages, LaTeX

References in corpus (29)

• String Theory and Noncommutative Geometry
• Noncommutative Geometry and Matrix Theory: Compactification on Tori
• Noncommutative Perturbative Dynamics
• A Gravity Theory on Noncommutative Spaces
• Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
• Noncommutative Geometry and Gravity
• Perturbative analysis on infrared aspects of noncommutative QED on R^4
• Enveloping algebra valued gauge transformations for non-abelian gauge groups on non-commutative spaces
• The One-loop UV Divergent Structure of U(1) Yang-Mills Theory on Noncommutative R^4
• Morita equivalence and duality
• Duality in Scalar Field Theory on Noncommutative Phase Spaces
• Non-renormalizability of θ-expanded noncommutative QED
• Twisted Gauge Theories
• An Invariant Action for Noncommutative Gravity in Four-Dimensions
• SL(2,C) Gravity with Complex Vierbein and Its Noncommutative Extension
• Lie algebraic Noncommutative Gravity
• Dualities of the Matrix Model from T-Duality of the Type II String
• Renormalizability of noncommutative SU(N) gauge theory
• The one-loop renormalization of the gauge sector in the noncommutative standard model
• Differential Calculus on Iso_q (N), Quantum Poincare' Algebra and q - Gravity
• Noncommutative supergravity in D=3 and D=4
• Twist to close
• The Lagrangian of q-Poincare' Gravity
• Noncommutative Symmetries and Gravity
• Twisted Covariant Noncommutative Self-dual Gravity
• Noncommutative QFT and Renormalization
• A nontrivial solvable noncommutative ϕ^3 model in 4 dimensions
• Theta-twisted Gravity
• Twisted invariances of noncommutative gauge theories

Cited by in corpus (57)

• Non-Geometric Fluxes, Quasi-Hopf Twist Deformations and Nonassociative Quantum Mechanics
• Noncommutative Gravity Solutions
• Testing Quantum Gravity by Quantum Light
• Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity
• Noncommutative supergravity in D=3 and D=4
• Noncommutative gravity coupled to fermions: second order expansion via Seiberg-Witten map
• Noncommutative Scalar Quasinormal Modes of the Reissner Nordström Black Hole
• Noncommutative gravity at second order via Seiberg-Witten map
• NC $SO(2,3{)}_{\star }$ gravity: noncommutativity as a source of curvature and torsion
• A twisted look on kappa-Minkowski: U(1) gauge theory
• Noncommutative scalar field in the non-extremal Reissner-Nordström background: QNM spectrum
• Gauge theories on quantum spaces
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• K-Poincare-Hopf algebra and Hopf algebroid structure of phase space from twist
• Nonassociative geometry in quasi-Hopf representation categories II: Connections and curvature
• 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
• Four-dimensional Gravity on a Covariant Noncommutative Space
• AdS-inspired noncommutative gravity on the Moyal plane
• Braided Symmetries in Noncommutative Field Theory
• On some models of geometric noncommutative general relativity
• Experimental Quantum Enhanced Optical Interferometry
• OSp(1|4) supergravity and its noncommutative extension
• Noncommutativity and logarithmic correction to the black hole entropy
• Four-Dimensional Gravity on a Covariant Noncommutative Space (II)
• Noncommutative gauge fields coupled to noncommutative gravity
• Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space
• Noncommutative Gauge Theory and Gravity in Three Dimensions
• SL(2,C) gravity on noncommutative space with Poisson structure
• Noncommutative gravity and the relevance of the $\theta$-constant deformation
• Extended gravity theories from dynamical noncommutativity
• Noncommutative gravity with self-dual variables
• Covariant hamiltonian for gravity coupled to $p$-forms
• Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes
• Noncommutative gauge and gravity theories and geometric Seiberg-Witten map
• Noncommutative Electrodynamics from $SO(2,3{)}_{\star }$ Model of Noncommutative Gravity
• Gravity as a Gauge Theory on Three-Dimensional Noncommutative spaces
• Intertwining noncommutativity with gravity and particle physics
• Background independent noncommutative gravity from Fedosov quantization of endomorphism bundle
• Dirac field and gravity in NC $SO(2,3{)}_{\star }$ model
• Noncommutative Solitons of Gravity
• Thermodynamic Properties of Yukawa-Schwarzschild Black Hole in Non-commutative Gauge Gravity
• Phase space quantization, noncommutativity and the gravitational field
• T-Dualities and Doubled Geometry of the Principal Chiral Model
• BV quantization of dynamical fuzzy spectral triples
• Self-dual road to noncommutative gravity with twist: a new analysis
• A Simple Model of Double Dynamics on Lie Groups
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• Noncommutative $SO(2,3{)}_{\star }$ Gauge Theory of Gravity
• $\kappa$-General-Relativity I: a Non-Commutative GR Theory with the $\kappa$-Minkowski Spacetime as its Flat Limit
• Commutative deformations of general relativity: nonlocality, causality, and dark matter
• Gauge theory on kappa-Minkowski revisited: the twist approach
• Entropy of black holes, charged probes and noncommutative generalization
• Noncommutative hamiltonian formalism for noncommutative gravity
• A bigravity model from noncommutative geometry
• Noncommutative $D=5$ Chern-Simons Gravity: Kaluza-Klein Reduction and Chiral Gravitational Anomaly