Gravity on a fuzzy sphere

TL;DR

This paper introduces a matrix model-based action for gravity on a fuzzy sphere, revealing similarities with noncommutative plane gravity, including gauge transformation structures and deformations of classical diffeomorphisms.

Contribution

It develops a novel matrix model formulation of gravity on a fuzzy sphere, highlighting its relation to noncommutative 2D gravity models.

Findings

Solution space spanned by pure U(2) gauge transformations

Existence of deformations of classical diffeomorphisms

Striking similarities with noncommutative plane gravity

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.