Lattice Realizations of Flat Gauging and T-duality Defects at Any Radius

TL;DR

This paper investigates non-invertible topological defects in the 2D compact boson, demonstrating their persistence under discretization and their unique properties like non-compact edge modes and infinite quantum dimension.

Contribution

It introduces a lattice approach to analyze exotic defects from gauging symmetries, revealing their continuous spectra and methods to achieve finite quantum dimensions.

Findings

All topological interfaces survive discretization.

Non-compact edge modes lead to infinite quantum dimension.

Modifications for rational radii yield standard defects.

Abstract

We analyze non-invertible topological interfaces and defects in the two-dimensional compact boson, focusing on the more exotic ones obtained by gauging continuous symmetries with flat connections on a half-space. These include interfaces between mutually irrational radii and T-duality symmetries at arbitrary boson radius. Using the modified Villain discretization on both a Euclidean two-dimensional square lattice and a quantum one-dimensional chain, we show that all these topological interfaces survive discretization and give rise to non-compact edge modes localized at the defect sites. Such non-compact edge modes imply a continuous defect spectrum and an infinite quantum dimension. In the special case of rational radii, we show how the defect action or Hamiltonian can be modified in order to compactify the edge modes and produce more standard defects with finite quantum dimension.