Model knot solutions for the twisted Bogomolny equations

Abstract

In this paper we prove existence for model knot solutions to the dimensionally reduced twisted Kapustin-Witten equations on ${\mathbb{R}}_{+}^3$ for any twisting parameter $t\in (0,\infty )$. We start with the explicit solutions for $t=1$ derived in \cite{WFivebranes} and perform a continuity argument in $t$. This corroborates a prediction of Gaiotto and Witten \cite[][p. 961]{GW}.