The Chern-Simons One-form and Gravity on a Fuzzy Space

Details The Chern-Simons One-form and Gravity on a Fuzzy Space The Chern-Simons One-form and Gravity on a Fuzzy Space

2006-04-29

arxiv.org/abs/hep-th/0605008v2

Nucl.Phys.B750:321-333,2006

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, references added

Scientific paper

10.1016/j.nuclphysb.2006.06.009

The one-dimensional ${\cal N}\times {\cal N}$-matrix Chern-Simons action is given, for large ${\cal N}$ and for slowly varying fields, by the $(2k+1)$-dimensional Chern-Simons action $S_{CS}$, where the gauge fields in $S_{CS}$ parametrize the different ways in which the large ${\cal N}$ 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 ${\cal N}$ and by the higher dimensional Chern-Simons action when the fuzzy space is approximated by a continuous manifold.

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