1205.0046 (Kazutoshi Ohta et al.)

Non-Abelian Localization for Supersymmetric Yang-Mills-Chern-Simons
Theories on Seifert Manifold    [PDF]

Kazutoshi Ohta, Yutaka Yoshida

We derive non-Abelian localization formulae for supersymmetric Yang-Mills-Chern-Simons theory with matters on a Seifert manifold M, which is the three-dimensional space of a circle bundle over a two-dimensional Riemann surface \Sigma, by using the cohomological approach introduced by Kallen. We find that the partition function and the vev of the supersymmetric Wilson loop reduces to a finite dimensional integral and summation over classical flux configurations labeled by discrete integers. We also find the partition function reduces further to just a discrete sum over integers in some cases, and evaluate the supersymmetric index (Witten index) exactly on S^1x\Sigma. The index completely agrees with the previous prediction from field theory and branes. We discuss a vacuum structure of the ABJM theory deduced from the localization.

View original: http://arxiv.org/abs/1205.0046