Symmetry, Gravity and Noncommutativity

Abstract

We review some aspects of the implementation of spacetime symmetries in noncommutative field theories, emphasizing their origin in string theory and how they may be used to construct theories of gravitation. The geometry of canonical noncommutative gauge transformations is analysed in detail and it is shown how noncommutative Yang-Mills theory can be related to a gravity theory. The construction of twisted spacetime symmetries and their role in constructing a noncommutative extension of general relativity is described. We also analyse certain generic features of noncommutative gauge theories on D-branes in curved spaces, treating several explicit examples of superstring backgrounds.

52 pages; Invited review article to be published in Classical and Quantum Gravity; v2: references added

References in corpus (7)

• A Gravity Theory on Noncommutative Spaces
• Second Order Noncommutative Corrections to Gravity
• A note on the noncommutative correction to gravity
• Remarks on twisted noncommutative quantum field theory
• Gravity and the Structure of Noncommutative Algebras
• The Chern-Simons One-form and Gravity on a Fuzzy Space
• Noncommutative Field Theory on Homogeneous Gravitational Waves

Cited by in corpus (30)

• Kappa-Minkowski space-time and the star product realizations
• Covariant realizations of kappa-deformed space
• Emergent Gravity from Noncommutative Spacetime
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Twisting all the way: from Classical Mechanics to Quantum Fields
• Lie algebraic Noncommutative Gravity
• Three Dimensional Quantum Geometry and Deformed Poincare Symmetry
• Position-dependent noncommutativity in quantum mechanics
• Deformed Reissner--Nordstrom solutions in noncommutative gravity
• Emergent Spacetime and The Origin of Gravity
• Noncommutative corrections to classical black holes
• Tunneling between de Sitter and anti de Sitter black holes in a noncommutative D3-brane formalism
• Spherically Symmetric Noncommutative Space: d = 4
• The deformation quantizations of the hyperbolic plane
• Finite temperature phase transition of a single scalar field on a fuzzy sphere
• Twisted Covariant Noncommutative Self-dual Gravity
• Dynamical noncommutativity and Noether theorem in twisted phi^*4 theory
• Noncommutative Electromagnetism As A Large N Gauge Theory
• Symmetry Reduction in Twisted Noncommutative Gravity with Applications to Cosmology and Black Holes
• The supermembrane with central charges:(2+1)-D NCSYM, confinement and phase transition
• Conceptual Unification of Gravity and Quanta
• Gauge Theory of the Star Product
• Noncommutative Effects in the Black Hole Evaporation in Two Dimensions
• Duality and Braiding in Twisted Quantum Field Theory
• Twisted invariances of noncommutative gauge theories
• Twist Quantization of String and B Field Background
• Quantization of the open string on plane-wave limits of dS_n x S^n and non-commutativity outside branes
• Wilson Loops and Area-Preserving Diffeomorphisms in Twisted Noncommutative Gauge Theory
• Nonabelian localization for gauge theory on the fuzzy sphere