Invertible defects and isomorphisms of rational CFTs

TL;DR

This paper establishes a one-to-one correspondence between invertible topological defects and conformal isomorphisms in rational CFTs, showing their equivalence when both preserve rational symmetry.

Contribution

It proves that invertible topological defects correspond exactly to conformal isomorphisms in rational CFTs, extending understanding of symmetries and dualities in these theories.

Findings

Invertible topological defects correspond to conformal isomorphisms.

The correspondence preserves composition of defects and isomorphisms.

Applicable to rational CFTs with preserved rational symmetry.

Abstract

Given two two-dimensional conformal field theories, a domain wall -- or defect line -- between them is called invertible if there is another defect with which it fuses to the identity defect. A defect is called topological if it is transparent to the stress tensor. A conformal isomorphism between the two CFTs is a linear isomorphism between their state spaces which preserves the stress tensor and is compatible with the operator product expansion. We show that for rational CFTs there is a one-to-one correspondence between invertible topological defects and conformal isomorphisms if both preserve the rational symmetry. This correspondence is compatible with composition.