Yang-Mills theory and a superquadric

TL;DR

This paper constructs a supermanifold related to superquadrics and establishes a connection between a Chern-Simons type theory on this manifold and N=3, D=4 Yang-Mills theory, suggesting a new geometric approach to gauge theories.

Contribution

It introduces a supermanifold model that links supergeometry with N=3, D=4 Yang-Mills theory via a conjectured equivalence involving Chern-Simons theory.

Findings

Supermanifold ST constructed as an open subset of a superquadric.

Dolbeault algebra Omega^{0*}(ST) is quasiisomorphic to N=3, D=4 YM algebra.

Conjectured equivalence between Chern-Simons theory on ST and N=3, D=4 YM theory.

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.