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

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 field...

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Bibliographic Details
Published in:Nuclear physics. B 2006-08, Vol.750 (3), p.321-333
Main Author: Nair, V.P.
Format: Article
Language:English
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Summary: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.
ISSN:0550-3213
1873-1562
DOI:10.1016/j.nuclphysb.2006.06.009