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.
Gravity on a fuzzy sphere / P. VALTANCOLI. - In: INTERNATIONAL JOURNAL OF MODERN PHYSICS A. - ISSN 0217-751X. - STAMPA. - 19:(2004), pp. 361-370.
Gravity on a fuzzy sphere
VALTANCOLI, PAOLO
2004
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.
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