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

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