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arXiv · 0711.4235

On relationships among Chern-Simons theory, BF theory and matrix model

Takaaki Ishii·Goro Ishiki·Kazutoshi Ohta·Shinji Shimasaki·Asato Tsuchiya
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Abstract

Chern-Simons theory on a U(1) bundle over a Riemann surface Σ_g of genus g is dimensionally reduced to BF theory with a mass term, which is equivalent to the two-dimensional Yang-Mills on Σ_g. We show that the former is inversely obtained from the latter by the extended matrix T-duality developed in hep-th/0703021. For the case of g=0 (i.e. S^2), the U(1) bundle represents the lens space S^3/Z_p. We find that in this case both the Chern-Simons theory and the BF theory with the mass term are realized in a matrix model. We also construct Wilson loops in the matrix model that correspond to those in the Chern-Simons theory on S^3.

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Takaaki Ishii, Goro Ishiki, Kazutoshi Ohta, Shinji Shimasaki, Asato Tsuchiya. 2008-05-30. On relationships among Chern-Simons theory, BF theory and matrix model. https://doi.org/10.1143/ptp.119.863

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