't Hooft Operators in the Boundary

TL;DR

This paper extends the construction of 't Hooft operators in boundary conditions of supersymmetric Yang-Mills theory from rank one gauge groups to arbitrary gauge groups, providing explicit solutions for certain magnetic charges.

Contribution

It generalizes the known 't Hooft operator constructions to any gauge group G, including explicit solutions for specific magnetic charges.

Findings

Extended 't Hooft operator construction to arbitrary gauge groups G.

Provided closed-form solutions for certain magnetic charges.

Facilitates applications in knot theory on three-manifolds.

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.