Noncommutative gravity: fuzzy sphere and others

Abstract

Gravity on noncommutative analogues of compact spaces can give a finite mode truncation of ordinary commutative gravity. We obtain the actions for gravity on the noncommutative two-sphere and on the noncommutative ${\mathbf{CP}}^2$ in terms of finite dimensional $(N\times N)$-matrices. The commutative large $N$ limit is also discussed.

LaTeX, 13 pages, section on CP^2 added + minor changes