On Exceptional 't Hooft Lines in 4D-Chern-Simons Theory

TL;DR

This paper investigates 't Hooft lines and their associated operators in 4D Chern-Simons theory with exceptional gauge groups E6 and E7, providing oscillator realizations and topological gauge quivers.

Contribution

It introduces new oscillator realizations of 't Hooft lines for exceptional groups and proposes topological gauge quivers encoding their properties.

Findings

Oscillator realizations for 't Hooft lines in E6 and E7

Topological gauge quivers encoding line properties

Interpretation of Darboux coordinates in topological matter

Abstract

We study 't Hooft lines and the associated $\mathcal{L}$- operators in topological 4D Chern-Simons theory with gauge symmetry given by the exceptional groups E$_{6}$ and E$_{7}$. We give their oscillator realisations and propose topological gauge quivers encoding the properties of these topological lines where Darboux coordinates are interpreted in terms of topological fundamental matter. Other related aspects are also described.