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

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

2007-11-27

arxiv.org/abs/0711.4235v2

Prog.Theor.Phys.119:863-882,2008

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, references added, typos corrected

Scientific paper

10.1143/PTP.119.863

Chern-Simons theory on a U(1) bundle over a Riemann surface \Sigma_g of genus g is dimensionally reduced to BF theory with a mass term, which is equivalent to the two-dimensional Yang-Mills on \Sigma_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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