The Line, the Strip and the Duality Defect

TL;DR

This paper constructs and analyzes non-invertible duality defects in exotic topological models, revealing continuous and discrete symmetry structures and their implications in symmetry topological field theories.

Contribution

It introduces codim-1 condensation defects via higher gauging in SymTFT, demonstrating non-invertible duality symmetries in XY-plaquette and XYZ-cube models, including a novel continuous SO(2) symmetry.

Findings

XY-plaquette admits a θ-term.

Condensation defects realize non-invertible self-duality symmetries.

XY-plaquette exhibits a non-invertible continuous SO(2) symmetry.

Abstract

In the Symmetry Topological Field Theories (SymTFT) that describes the exotic models XY-plaquette and XYZ-cube, we construct codim-1 condensation defects by higher gauging with discrete torsion the non-compact symmetry of the bulk. In the framework of SymTFT Mille-feuille, which captures the Lorentz-invariance breaking subsystem symmetries, these models are dual to foliated versions of Maxwell theory. We show first that the XY-plaquette model admits a $\theta$-term. Then, we show these condensation defects realize non-invertible self-duality symmetries at any value of the coupling. In the XYZ-cube model such symmetry is discrete. On the other hand, we find that the XY-plaquette has a non-invertible continuous $SO(2)$ symmetry, thus extending the results in the current literature.