Eliminating the Higgs field and perturbing Yang-Mills connections in cone Yang-Mills theory

Abstract

We study the configurations of the cone Yang-Mills functional over a closed connected manifold. We show that the Euler-Lagrange equation from variations in the Higgs field is always uniquely solvable for $ζ\neq 0$, allowing us to eliminate one of the two equations from the theory. By eliminating the equation, we obtain a family of ``effective cone Yang-Mills functionals'' on the space of connection 1-forms indexed by $ζ$, which reduce to Yang-Mills theory when $ζ= 0$. This suggests a way to nontrivially deform the Yang-Mills moduli space. We take the first step towards this deformation by showing that, near certain critical points of the Yang-Mills functional, there is a family of smooth connections $A_t$ which satisfy the $tζ$-cone Yang-Mills equations.