The Chern-Simons One-form and Gravity on a Fuzzy Space
arXiv:hep-th/0605008 · doi:10.1016/j.nuclphysb.2006.06.009
Abstract
The one-dimensional -matrix Chern-Simons action is given, for large and for slowly varying fields, by the -dimensional Chern-Simons action , where the gauge fields in parametrize the different ways in which the large 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 and by the higher dimensional Chern-Simons action when the fuzzy space is approximated by a continuous manifold.
16 pages, references added