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.
"Invertible defects and isomorphisms of rational CFTs." Adv. Theor. Math. Phys. 15 (1) 43 - 69, January 2011.