Gravitational fields on a noncommutative space

Abstract

Noncommutative three-dimensional gravity can be described in terms of a noncommutative Chern-Simons theory. We extend this structure and also propose an action for gravitational fields on an even dimensional noncommutative space. The action is worked out in some detail for fields on a noncommutative ${\mathbf{CP}}^2$ and on $S^4$.

LaTeX, 16 pages, section 2 rewritten for clarity

Cited by in corpus (22)

• Symmetry, Gravity and Noncommutativity
• An Invariant Action for Noncommutative Gravity in Four-Dimensions
• Quantum Hall Effect in Higher Dimensions, Matrix Models and Fuzzy Geometry
• The effective action for edge states in higher dimensional quantum Hall systems
• Noncommutative Self-dual Gravity
• Edge States for quantum Hall droplets in higher dimensions and a generalized WZW model
• Noncommutative Topological Theories of Gravity
• Noncommutative gravity: fuzzy sphere and others
• Dirac Operators on Coset Spaces
• Drinfeld Twist and General Relativity with Fuzzy Spaces
• The Chern-Simons One-form and Gravity on a Fuzzy Space
• Non Commutative Bianchi type II Quantum Cosmology
• Chiral spinors and gauge fields in noncommutative curved space-time
• Spherically symmetric monopoles in noncommutative space
• Noncommutative Gauge Theory and Gravity in Three Dimensions
• Inherent Holography In Fuzzy Spaces and An N-tropic Approach To The Cosmological Constant Problem
• Scalar field in the Bianchi I: Non commutative classical and Quantum Cosmology
• Gravity as a Gauge Theory on Three-Dimensional Noncommutative spaces
• WKB-type Approximation to Noncommutative Quantum Cosmology
• Intertwining noncommutativity with gravity and particle physics
• Strings, Dipoles and Fuzzy Spheres
• Gauge theory models on $\kappa$-Minkowski space: Results and prospects