Non-Invertible T-duality at Any Radius via Non-Compact SymTFT

TL;DR

This paper generalizes T-duality for the 2d compact boson at any radius, introducing non-invertible symmetries via topological manipulations and symmetry TFT, unifying discrete T-duality symmetries.

Contribution

It constructs non-invertible T-duality symmetries at arbitrary radii using topological manipulations and symmetry TFT, extending previous invertible cases.

Findings

Generated the entire circle branch of the $c=1$ conformal manifold.

Identified the topological operator as an open condensation defect.

Reduced to known T-duality defect for rational square radii.

Abstract

We extend the construction of the T-duality symmetry for the 2d compact boson to arbitrary values of the radius by including topological manipulations such as gauging continuous symmetries with flat connections. We show that the entire circle branch of the $c=1$ conformal manifold can be generated using these manipulations, resulting in a non-invertible T-duality symmetry when the gauging sends the radius to its inverse value. Using the recently proposed symmetry TFT describing continuous global symmetries of the boundary theory, we identify the topological operator corresponding to these new T-duality symmetries as an open condensation defect of the bulk theory, constructed by (higher) gauging an $\mathbb{R}$ subgroup of the bulk global symmetries. Notably, when the boundary theory is the compact boson with a rational square radius, this operator reduces to the familiar T-duality defect described by a Tambara-Yamagami fusion category. This construction thus naturally includes all possible discrete T-duality symmetries of the theory in a unified way.