Monodromy Defects for Electric-Magnetic Duality, Hyperbolic Space, and Lines
TLDR
This paper investigates monodromy defects in Maxwell theory via conformal mapping to AdS3 x S1, recovering defect primaries and analyzing Wilson/'t Hooft line interactions.
Key contributions
- Explores monodromy defects for non-invertible symmetries in Maxwell theory.
- Recovers the spectrum of defect conformal primaries using AdS3 x S1 mapping.
- Analyzes Wilson/'t Hooft line behavior, including termination and decomposability.
- Shows lines behave topologically near defects, governed by Chern-Simons theory.
Why it matters
This research advances our understanding of non-invertible symmetries and their associated defects in Maxwell theory. By detailing the behavior of fundamental lines near these defects, it provides new insights into topological aspects of quantum field theories. This work could inform future studies in theoretical physics.
Original 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.
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