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

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.