Defect Conformal Manifolds from Phantom Noninvertible Symmetries

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 noninvertible-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.