An Energy Gap for Complex Yang-Mills Equations

TL;DR

This paper extends the concept of an energy gap from pure Yang-Mills equations to complex Yang-Mills equations on certain Riemannian manifolds, demonstrating a new stability property in gauge theory.

Contribution

It proves an energy gap result for complex Yang-Mills equations using existing results from pure Yang-Mills equations, under specific geometric conditions.

Findings

Established an energy gap for complex Yang-Mills equations

Extended the application of energy gap results to complex gauge fields

Linked stability properties of complex and pure Yang-Mills solutions

Abstract

We use the energy gap result of pure Yang-Mills equation [Feehan P.M.N., Adv. Math. 312 (2017), 547-587, arXiv:1502.00668] to prove another energy gap result of complex Yang-Mills equations [Gagliardo M., Uhlenbeck K., J. Fixed Point Theory Appl. 11 (2012), 185-198, arXiv:1401.7366], when Riemannian manifold $X$ of dimension $n\geq 2$ satisfies certain conditions.