Monodromy Defects for Electric-Magnetic Duality, Hyperbolic Space, and Lines

TL;DR

This paper investigates monodromy defects in Maxwell theory, analyzing their conformal properties, effects on Wilson/'t Hooft lines, and their topological behavior governed by Chern-Simons theory.

Contribution

It introduces a detailed analysis of monodromy defects in Maxwell theory, including their spectrum, line interactions, and topological characteristics.

Findings

Lines can terminate on the defect.

Lines of unit electric/magnetic charge can be decomposed into elementary lines.

Lines behave as topological objects near the defect, governed by Chern-Simons theory.

Abstract

In this note we explore monodromy defects for non-invertible symmetries in Maxwell theory, exploiting the conformal mapping to $AdS_{3} \times S^{1}$. With this approach we recover the spectrum of the defect conformal primaries. We also dedicate some time discussing the behaviour of Wilson/'t Hooft lines in the presence of such a monodromy defect, and highlight the following aspects of their behaviour: i) the lines can terminate on the defect, ii) lines of the unit electric (magnetic) charge may seize to be indecomposable, and can be represented as integer powers of some more elementary lines, and iii) they behave as topological objects when brought close to the defect, and this behaviour is governed by a Chern-Simons theory.