Defect Conformal Manifolds from Phantom (Non-Invertible) Symmetries

TL;DR

This paper introduces a mechanism for (1+1)d conformal field theories to possess interface conformal manifolds without continuous symmetries, utilizing non-invertible symmetries in the folded theory, with applications to reflection coefficients and higher dimensions.

Contribution

It presents a novel symmetry-based approach to construct and analyze defect conformal manifolds in the absence of traditional symmetries, including explicit examples and generalizations.

Findings

Computed the evolution of reflection coefficients along defect conformal manifolds.

Demonstrated the role of non-invertible symmetries in (1+1)d CFTs.

Discussed higher-dimensional generalizations and no-go theorems.

Abstract

We explore a general mechanism that allows (1+1)d CFTs to have interesting interface conformal manifolds even in the absence of any continuous internal symmetry or supersymmetry. This is made possible by the breaking of an enhanced continuous symmetry, which is generically non-invertible, arising in the folded theory. We provide several examples and showcase the power of the symmetry-based approach by computing the evolution of the reflection coefficient along the defect conformal manifold. We also discuss higher-dimensional generalizations and we comment on no-go theorems.