$G_2$–instantons over asymptotically cylindrical manifolds

Abstract

A concrete model for a $7$–dimensional gauge theory under special holonomy is proposed, within the paradigm of Donaldson and Thomas, over the asymptotically cylindrical $G_2$–manifolds provided by Kovalev’s solution to a noncompact version of the Calabi conjecture.

One obtains a solution to the $G_2$–instanton equation from the associated Hermitian Yang–Mills problem, to which the methods of Simpson et al are applied, subject to a crucial asymptotic stability assumption over the “boundary at infinity”.