On 2d CFTs that interpolate between minimal models

Abstract

We investigate exactly solvable two-dimensional conformal field theories that exist at generic values of the central charge, and that interpolate between A-series or D-series minimal models. When the central charge becomes rational, correlation functions of these CFTs may tend to correlation functions of minimal models, or diverge, or have finite limits which can be logarithmic. These results are based on analytic relations between four-point structure constants and residues of conformal blocks.

30 pages, v3: restructuring and clarifications, in particular in the introduction

References in corpus (3)

• The analytic bootstrap equations of non-diagonal two-dimensional CFT
• The unitary subsector of generalized minimal models
• Notes on the solutions of Zamolodchikov-type recursion relations in Virasoro minimal models

Cited by in corpus (9)

• Geometrical four-point functions in the two-dimensional critical $Q$-state Potts model: The interchiral conformal bootstrap
• On four-point connectivities in the critical 2d Potts model
• Logarithmic CFT at generic central charge: from Liouville theory to the $Q$-state Potts model
• Coupled minimal models revisited
• Four-point geometrical correlation functions in the two-dimensional $Q$-state Potts model: connections with the RSOS models
• The non-rational limit of D-series minimal models
• Critical loop models are exactly solvable
• Coupled minimal models revisited II: Constraints from permutation symmetry
• Analytic conformal bootstrap and Virasoro primary fields in the Ashkin-Teller model