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Invertible defects and isomorphisms of rational CFTs

Davydov, Alexei and Kong, Liang and Runkel, Ingo (2011) Invertible defects and isomorphisms of rational CFTs. Advances in Theoretical and Mathematical Physics, 15 (1). pp. 43-69. ISSN 1095-0761.

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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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Additional Information:© 2012 International Press. Published January 2011. The authors would like to thank Jürgen Fuchs for helpful comments on a draft of this paper. AD thanks Max Planck Institut für Mathematik (Bonn) for hospitality and excellent working conditions. LK is supported in part by the Gordon and Betty Moore Foundation through Caltech’s Center for the Physics of Information, and by NSF Grant No. PHY-0803371, the Basic Research Young Scholars Program and the Initiative Scientific Research Program of Tsinghua University, and NSFC Grant No. 11071134.
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Gordon and Betty Moore FoundationUNSPECIFIED
Caltech Center for the Physics of InformationUNSPECIFIED
Basic Research Young Scholars ProgramUNSPECIFIED
Tsinghua UniversityUNSPECIFIED
National Natural Science Foundation of China11071134
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ID Code:32064
Deposited By: Aucoeur Ngo
Deposited On:25 Jun 2012 22:20
Last Modified:03 Oct 2019 03:57

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