1 On relationships among Chern-Simons theory, BF theory and matrix model
Takaaki Ishii, Goro Ishiki, Kazutoshi Ohta, Shinji Shimasaki, Asato Tsuchiya · 2013
Chern-Simons theory on a U(1) bundle over a Riemann surface Σg of genus g is dimensionally reduced to BF theory with a mass term, which is equivalent to the two-dimensional Yang-Mills on Σg. 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 /Zp. 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. Some matrix models have been proposed as nonperturbative formulation of superstring or M-theory. 1)–3) Since the information of topology is relevant for compactification in string theory, it should be included in these matrix models. The