Double Hodge Theory for a particle on Torus

Abstract

We investigate all possible nilpotent symmetries for a particle on torus. We explicitly construct four independent nilpotent BRST symmetries for such systems and derive the algebra between the generators of such symmetries. We show that such a system has rich mathematical properties and behaves as double Hodge theory. We further construct the finite field dependent BRST transformation for such systems by integrating the infinitesimal BRST transformation systematically. Such a finite transformation is useful in realizing the various theories with toric geometry.

14 pages. arXiv admin note: substantial text overlap with arXiv:1308.0982, text overlap with arXiv:hep-th/0312073 by other authors