Advances in Theoretical and Mathematical Physics

Volume 15 (2011)

Number 1

Invertible defects and isomorphisms of rational CFTs

Pages: 43 – 69



Alexei Davydov

Liang Kong

Ingo Runkel


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.

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