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 (2k+1)-dimensional Chern-Simons action S, where the gauge fields in S 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.
- Publication:
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Nuclear Physics B
- Pub Date:
- August 2006
- DOI:
- 10.1016/j.nuclphysb.2006.06.009
- arXiv:
- arXiv:hep-th/0605008
- Bibcode:
- 2006NuPhB.750..321N
- Keywords:
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- High Energy Physics - Theory
- E-Print:
- 16 pages, references added