A Novel Large-N Reduction on S^3: Demonstration in Chern-Simons Theory

Details A Novel Large-N Reduction on S^3: Demonstration in Chern-Simons Theory A Novel Large-N Reduction on S^3: Demonstration in Chern-Simons Theory

2010-01-27

arxiv.org/abs/1001.4917v1

Nucl.Phys.B834:423-452,2010

Physics

High Energy Physics

High Energy Physics - Theory

39 pages, 8 figures

Scientific paper

10.1016/j.nuclphysb.2010.02.026

We show that the planar Chern-Simons (CS) theory on S^3 can be described by its dimensionally reduced model. This description of CS theory can be regarded as a novel large-N reduction for gauge theories on S^3. We find that if one expands the reduced model around a particular background consisting of multiple fuzzy spheres, the reduced model becomes equivalent to CS theory on S^3 in the planar limit. In fact, we show that the free energy and the vacuum expectation value of unknot Wilson loop in CS theory are reproduced by the reduced model in the large-N limit.

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