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

Understand

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.