On relationships among Chern-Simons theory, BF theory and matrix model
High Energy Physics - Theory
2008-11-26 v2
Abstract
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.
Cite
@article{arxiv.0711.4235,
title = {On relationships among Chern-Simons theory, BF theory and matrix model},
author = {Takaaki Ishii and Goro Ishiki and Kazutoshi Ohta and Shinji Shimasaki and Asato Tsuchiya},
journal= {arXiv preprint arXiv:0711.4235},
year = {2008}
}
Comments
20 pages, references added, typos corrected