Some boundedness properties of solutions to the complex Yang-Mills equations on closed 4-manifolds

Abstract In this article, we study the analytical properties of the solutions of the complex Yang-Mills equations on a closed Riemannian four-manifold X with a Riemannian metric g. The main result is that if g is g o o d and the connection is an approximate ASD connection, then the extra field has a positive lower bound. As an application, we obtain some gap results for Yang-Mills connections and Kapustin-Witten equations.