Gravity on a fuzzy sphere

Abstract

We propose an action for gravity on a fuzzy sphere, based on a matrix model. We find striking similarities with an analogous model of two dimensional gravity on a noncommutative plane, i.e. the solution space of both models is spanned by pure U(2) gauge transformations acting on the background solution of the matrix model, and there exist deformations of the classical diffeomorphisms which preserve the two-dimensional noncommutative gravity actions.

14 pages, no figures, LaTeX

Cited by in corpus (8)

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• Drinfeld Twist and General Relativity with Fuzzy Spaces
• A note on the geometrical interpretation of quantum groups and non-commutative spaces in gravity
• Noncommutative Gauge Theory and Gravity in Three Dimensions
• Intertwining noncommutativity with gravity and particle physics
• (2 + 1) noncommutative gravity and conical spacetimes
• U(2) projectors and 't Hooft-Polyakov monopoles on a fuzzy sphere
• Gauge theory models on $\kappa$-Minkowski space: Results and prospects