Opers and the twisted Bogomolny equations

Abstract

In this paper, we study the dimensionally reduced twisted Kapustin-Witten equations on the product of a compact Riemann surface $\Sigma$ 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}.

26 pages

References in corpus (1)

• Classification of Nahm pole solutions of the Kapustin-Witten equations on $S^1\times \Sigma \times {\mathbb{R}}^{+}$