Limits and Degenerations of Unitary Conformal Field Theories

Abstract

In the present paper, degeneration phenomena in conformal field theories are studied. For this purpose, a notion of convergent sequences of CFTs is introduced. Properties of the resulting limit structure are used to associate geometric degenerations to degenerating sequences of CFTs, which, as familiar from large volume limits of non-linear sigma models, can be regarded as commutative degenerations of the corresponding ``quantum geometries''. As an application, the large level limit of the A-series of unitary Virasoro minimal models is investigated in detail. In particular, its geometric interpretation is determined.

arXiv comment57 pages, no figures; minor clarifications and reference added; final version to appear in Commun. Math. Phys

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• Higher-spin gauge theories in three spacetime dimensions
• The limit of N=(2,2) superconformal minimal models
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• Non-Abelian T-duality and Modular Invariance
• Non-commutative Weitzenboeck geometry, gerbe modules, and WZW branes