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Large N reduction for Chern-Simons theory on S^3 · Around

2009

Large N reduction for Chern-Simons theory on S^3

Ishiki, Goro, Shimasaki, Shinji, Tsuchiya, Asato

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We study a matrix model which is obtained by dimensional reduction of Chern-Simon theory on S^3 to zero dimension.

We find that expanded around a particular background consisting of multiple fuzzy spheres, it reproduces the original theory on S^3 in the planar limit.
This is viewed as a new type of the large N reduction generalized to curved space.

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For an interesting approach to this subject, see Ref. Hanada:2005vr

Cited in the paper.

For recent developments in alternative lattice approach to supersymmetric gauge theory, see Refs. Kanamori:2009dk

Cited in the paper.

M. Hanada, L. Mannelli and Y. Matsuo, arXiv:0905.2995 [hep-th], arXiv:0907.4937 [hep-th]

Cited in the paper.

For explicit forms of ℒ i {\cal L}_{i} and L i ( q ) L^{(q)}_{i} , see Refs. Ishii:2008ib ; Ishii:2008tm ; Ishii:2007sy ; Ishiki:2008vf

Cited in the paper.

Indeed, only the S U ( K ) SU(K) part agrees Ishiki:2008vf . However, the difference does not affect the following analysis

Cited in the paper.

2009

Closest in time.

G. Ishiki, K. Ohta, S. Shimasaki and A. Tsuchiya, Phys. Lett. B 672

2009

Closest in time.