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

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• Twisting all the way: from Classical Mechanics to Quantum Fields
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• Lie algebraic Noncommutative Gravity
• Three Dimensional Quantum Geometry and Deformed Poincare Symmetry
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• Thermodynamics and evaporation of a modified Schwarzschild black hole in a non--commutative gauge theory
• On The Correspondence Between Noncommuative Field Theory And Gravity
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• Finsler Black Holes Induced by Noncommutative Anholonomic Distributions in Einstein Gravity
• Emergent Spacetime and The Origin of Gravity
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• Power-law expansion of the Universe from the bosonic Lorentzian type IIB matrix model
• Braided $L_{\infty }$-Algebras, Braided Field Theory and Noncommutative Gravity
• A note on the geometrical interpretation of quantum groups and non-commutative spaces in gravity
• Noncommutative Electromagnetism As A Large N Gauge Theory
• Non-commutative deformation of Chern-Simons theory
• Towards A Background Independent Quantum Gravity
• Quantum field theory with the generalized uncertainty principle II: Quantum Electrodynamics
• Poisson gauge theory
• Gauge Theories on Deformed Spaces
• Braided Symmetries in Noncommutative Field Theory
• Quasinormal Modes in Noncommutative Schwarzschild black holes
• Emergent Geometry from Quantized Spacetime
• Test of Emergent Gravity
• Noncommutative gauge theories on D-branes in non-geometric backgrounds
• Diffeomorphism covariant star products and noncommutative gravity
• Symmetry Reduction in Twisted Noncommutative Gravity with Applications to Cosmology and Black Holes
• Quantum Gravity from Noncommutative Spacetime
• Quantum tunneling and spectroscopy of noncommutative inspired Kerr black hole
• Quantum complex scalar fields and noncommutativity
• Dynamical noncommutativity
• Resonant-bar detectors of gravitational wave as possible probe of the noncommutative structure of space
• Seiberg--Witten maps for $\mathbf{SO}(1,3)$ gauge invariance and deformations of gravity
• Field Theory on Curved Noncommutative Spacetimes
• A Non-Commutative Kalb-Ramond Black Hole
• Connecting dissipation and noncommutativity: A Bateman system case study
• Quantization of Emergent Gravity
• Geodesics, accretion disk, gravitational lensing, time delay, and effects on neutrinos induced by a non-commutative black hole
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• Notes on Emergent Gravity
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• Footprint of spatial noncommutativity in resonant detectors of gravitational wave
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• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
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