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Non-Invertible Defects in 5d, Boundaries and Holography

Jeremias Aguilera Damia, Riccardo Argurio, Eduardo Garcia-Valdecasas

TL;DR

The paper generalizes the construction of infinite non-invertible symmetries from ABJ anomalies to 5d gauge theories with a mixed 1-form/0-form anomaly, producing codimension-2 non-invertible defects labeled by rational angles via coupling to a 3d TQFT. It analyzes the fate of these defects in the presence of a 4d boundary, showing how boundary conditions and ABJ anomalies shape whether bulk defects become boundary non-invertible operators or map to invertible boundary sectors. The authors provide explicit Maxwell-Chern-Simons examples and extend the discussion to holographic (AdS5) setups, establishing precise links between bulk non-invertible defects and boundary ABJ structures, including higher-gauging on submanifolds. The work highlights a cohesive picture where non-invertible bulk defects and ABJ anomalies on the boundary cohere in holographic dualities, with implications for higher-dimensional symmetry structures and their boundary realizations.

Abstract

We show that very simple theories of abelian gauge fields with a cubic Chern-Simons term in 5d have an infinite number of non-invertible co-dimension two defects. They arise by dressing the symmetry operators of the broken electric 1-form symmetry with a suitable topological field theory, for any rational angle. We further discuss the same theories in the presence of a 4d boundary, and more particularly in a holographic setting. There we find that the bulk defects, when pushed to the boundary, have various different fates. Most notably, they can become co-dimension one non-invertible defects of a boundary theory with an ABJ anomaly.

Non-Invertible Defects in 5d, Boundaries and Holography

TL;DR

The paper generalizes the construction of infinite non-invertible symmetries from ABJ anomalies to 5d gauge theories with a mixed 1-form/0-form anomaly, producing codimension-2 non-invertible defects labeled by rational angles via coupling to a 3d TQFT. It analyzes the fate of these defects in the presence of a 4d boundary, showing how boundary conditions and ABJ anomalies shape whether bulk defects become boundary non-invertible operators or map to invertible boundary sectors. The authors provide explicit Maxwell-Chern-Simons examples and extend the discussion to holographic (AdS5) setups, establishing precise links between bulk non-invertible defects and boundary ABJ structures, including higher-gauging on submanifolds. The work highlights a cohesive picture where non-invertible bulk defects and ABJ anomalies on the boundary cohere in holographic dualities, with implications for higher-dimensional symmetry structures and their boundary realizations.

Abstract

We show that very simple theories of abelian gauge fields with a cubic Chern-Simons term in 5d have an infinite number of non-invertible co-dimension two defects. They arise by dressing the symmetry operators of the broken electric 1-form symmetry with a suitable topological field theory, for any rational angle. We further discuss the same theories in the presence of a 4d boundary, and more particularly in a holographic setting. There we find that the bulk defects, when pushed to the boundary, have various different fates. Most notably, they can become co-dimension one non-invertible defects of a boundary theory with an ABJ anomaly.
Paper Structure (8 sections, 53 equations, 3 figures)

This paper contains 8 sections, 53 equations, 3 figures.

Table of Contents

  1. Introduction and Summary
  2. Non-invertible symmetries from ABJ anomalies in 4d
  3. Non-invertible 1-form symmetries in 5d
  4. Simple examples in Maxwell-Chern-Simons theory
  5. Adding boundaries
  6. Maxwell Theory
  7. Maxwell-Chern-Simons Theories
  8. Implications for holography

Figures (3)

  • Figure 1: a) A non-invertible topological operator ${\cal D}_{1/N}$ generating a non-trivial holonomy on the linking cycle $\gamma$ has a surface $\Sigma_4$ attached to it. b) A magnetic surface $T(\Gamma_2)$ intersects $\Sigma_4$ along $\gamma^{\prime}$. A flux is attached in $\Sigma_2$ such that $\partial\Sigma_2 = \gamma^{\prime}$.
  • Figure 2: Artistic impression of 5d Maxwell Theory with boundaries. Wilson lines $W_R$ charged under $U(1)^{(1)}_e$ may end on the boundary, generating $U(1)_{\partial}^{(0)}$.
  • Figure 3: