Noncommutative Two Dimensional Gravities

Abstract

We give formulations of noncommutative two dimensional gravities in terms of noncommutative gauge theories. We survey their classical solutions and show that solutions of the corresponding commutative theories continue to be solutions in the noncommutative theories as well. We argue that the existence of ``twisted'' diffeomorphisms, recently introduced in hep-th/0504183, is crucial for this conclusion.

13 pages, LaTeX, corrected typos, added references

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Cited by in corpus (30)

• Kappa-Minkowski space-time and the star product realizations
• Noncommutative Gravity
• Emergent Gravity from Noncommutative Spacetime
• Twisted Gauge Theories
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• Noncommutative BTZ Black Hole and Discrete Time
• Geodesic equation in $k$-Minkowski spacetime
• Newton's Equation on the kappa space-time and the Kepler problem
• $\kappa$-deformed Dirac Equation
• Gauge theories on quantum spaces
• Effects of Noncommutativity on the Black Hole Entropy
• Drinfeld Twist and General Relativity with Fuzzy Spaces
• Quantum statistics and noncommutative black holes
• Diffeomorphism covariant star products and noncommutative gravity
• $\kappa$-Minkowski star product in any dimension from symplectic realization
• Entanglement Entropy Renormalization for the NC scalar field coupled to classical BTZ geometry
• Uniformly accelerated detector in the $\kappa$-deformed Dirac vacuum
• Noncommutative correction to the entropy of charged BTZ black hole
• Thermofield dynamics and Gravity
• Contravariant Gravity on Poisson Manifolds and Einstein Gravity
• Particle Classification and Dynamics in GL(2,C) Gravity
• Phase structure of fuzzy black holes
• Wilson Loops and Area-Preserving Diffeomorphisms in Twisted Noncommutative Gauge Theory
• On the Quantization of Length in Noncommutative Spaces
• Newtonian cosmology and Evolution of kappa-deformed universe
• Deformed Kac-Moody Algebra and Noncommutative Fermi Theory in Two-Dimensions
• Entropy of black holes, charged probes and noncommutative generalization
• Gauge theory models on $\kappa$-Minkowski space: Results and prospects
• Quantization of Length in Spaces with Position-Dependent Noncommutativity
• On the Non-Flatness Nature of Noncommutative Minkowski Spacetime and the Singular Behavior of Probes