Yang-Mills theory and a superquadric
High Energy Physics - Theory
2008-10-20 v2
Abstract
We construct a supermanifold ST which turns to be an open subset of a superquadric Q(5|6) subset P^{3|3}times P^{3|3}. The Dolbeault algebra Omega^{0*}(ST) is quasiisomorphic to N=3, D=4 YM algebra in Batalin-Vilkovisky formulation. We construct a dbar-closed functional tr:Omega^{0*}(ST)=>C. We conjecture that Chern-Simons theory associated with a triple Omega^{0*}(ST)\otimes Mat_n,dbar,tr tr_{Mat_n}) is equivalent to N=3, D=4 YM theory with gauge group U_n in euclidean signature.
Cite
@article{arxiv.hep-th/0411111,
title = {Yang-Mills theory and a superquadric},
author = {M. Movshev},
journal= {arXiv preprint arXiv:hep-th/0411111},
year = {2008}
}
Comments
Final version. Will be published in "Algebra, Arithmetic and Geometry - Manin Festschrift"