The Chern-Simons one-form and gravity on a fuzzy space

The one-dimensional N x N-matrix Chem-Simons action is given, for large N and for slowly varying fields, by the (2k + 1)-dimensional Chem-Simons action S-CS, where the gauge fields in S-CS parametrize the different ways in which the large N limit can be taken. Since some of these gauge fields correspond to the isometrics of the space, we argue that gravity on fuzzy spaces can be described by the one-dimensional matrix Chem-Simons action at finite N and by the higher dimensional Chem-Simons action when the fuzzy space is approximated by a continuous manifold. (c) 2006 Elsevier B.V. All fights reserved.