Yang-Mills theory and a superquadric

Details Yang-Mills theory and a superquadric Yang-Mills theory and a superquadric

2004-11-10

arxiv.org/abs/hep-th/0411111v2

Physics

High Energy Physics

High Energy Physics - Theory

Final version. Will be published in "Algebra, Arithmetic and Geometry - Manin Festschrift"

Scientific paper

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.

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