't Hooft Operators in the Boundary

Abstract

We consider a topologically twisted maximally supersymmetric Yang-Mills theory on a four-manifold of the form $V=W\times {\mathbb{R}}_{+}$. 't Hooft disorder operators localized in the boundary component at finite distance of $V$ are relevant for the study of knot theory on the three-manifold $W$, and have recently been constructed for a gauge group of rank one. We extend this construction to an arbitrary gauge group $G$. For certain values of the magnetic charge of the 't Hooft operator, the solutions are obtained by embedding the rank one solutions in $G$ and can be given in closed form.

9 pages

References in corpus (2)

• Knot Invariants from Four-Dimensional Gauge Theory
• Boundary conditions for GL-twisted N=4 SYM

Cited by in corpus (4)

• On the Solutions of Generalized Bogomolny Equations
• Solutions of Kapustin-Witten equations for ADE-type groups
• On BPS Strings in $\mathcal{N}=4$ Yang-Mills Theory
• Inner Product in Highest-Weight Representation