Opers and the twisted Bogomolny equations

In this paper, we study the dimensionally reduced twisted Kapustin-Witten equations on the product of a compact Riemann surface $\mathrm{\Sigma }$ with ${\mathbb{R}}^{+}$. The main result is a Kobayashi-Hitchin type correspondence between the space of tilted Nahm pole solutions and the moduli space of Beilinson-Drinfeld opers. This corroborates a prediction of Gaiotto and Witten \cite[p.971]{gaiotto2012knot}.