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

Abstract

The one-dimensional N × N -matrix Chern–Simons action is given, for large N and for slowly varying fields, by the ( 2 k + 1 ) -dimensional Chern–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 isometries of the space, we argue that gravity on fuzzy spaces can be described by the one-dimensional matrix Chern–Simons action at finite N and by the higher dimensional Chern–Simons action when the fuzzy space is approximated by a continuous manifold.