Energy bound for Kapustin-Witten solutions on $S^3\times {\mathbb{R}}^{+}$

Abstract

We consider solutions of Kapustin-Witten equation with Nahm pole boundary on $S^3\times {\mathbb{R}}^{+}$. These solutions are usually called Nahm pole solutions. In this paper, we will prove that there exists a constant $C>0$ such that $\Vert F_A{\Vert }_{L^2}\le C$ for any Nahm pole solution $(A,\varphi )$.

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