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Limits and Degenerations of Unitary Conformal Field Theories

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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.

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Correspondence to Daniel Roggenkamp.

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Communicated by M.R. Douglas

Acknowledgements It is a pleasure to thank Gavin Brown, Jarah Evslin, José Figueroa-O’Farrill, Matthias Gaberdiel, Maxim Kontsevich, Werner Nahm, Andreas Recknagel, Michael Rösgen, Volker Schomerus, Gérard Watts and the referee for helpful comments or discussions. We also wish to thank the “Abdus Salam International Center for Theoretical Physics” for hospitality, since part of this work was performed there.

D. R. was supported by DFG Schwerpunktprogramm 1096 and by the Marie Curie Training Site “Strings, Branes and Boundary Conformal Field Theory” at King’s College London, under EU grant HPMT-CT-2001-00296. K. W. was partly supported under U.S. DOE grant DE-FG05-85ER40219, TASK A, at the University of North Carolina at Chapel Hill.

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Roggenkamp, D., Wendland, K. Limits and Degenerations of Unitary Conformal Field Theories. Commun. Math. Phys. 251, 589–643 (2004).

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