The non-rational limit of D-series minimal models

Abstract

We study the limit of D-series minimal models when the central charge tends to a generic irrational value $c\in (-\infty ,1)$. We find that the limit theory's diagonal three-point structure constant differs from that of Liouville theory by a distribution factor, which is given by a divergent Verlinde formula. Nevertheless, correlation functions that involve both non-diagonal and diagonal fields are smooth functions of the diagonal fields' conformal dimensions. The limit theory is a non-trivial example of a non-diagonal, non-rational, solved two-dimensional conformal field theory.

27 pages, v4: Corrected global sign in Eq. (2.25)

References in corpus (4)

• On four-point connectivities in the critical 2d Potts model
• Fermionic CFTs and classifying algebras
• The analytic bootstrap equations of non-diagonal two-dimensional CFT
• On 2d CFTs that interpolate between minimal models

Cited by in corpus (6)

• Geometrical four-point functions in the two-dimensional critical $Q$-state Potts model: The interchiral conformal bootstrap
• Coupled minimal models revisited II: Constraints from permutation symmetry
• Three- and four-point connectivities of two-dimensional critical $Q-$ Potts random clusters on the torus
• Anyon Condensation in Virasoro TQFT: Wormhole Factorization
• On the Virasoro fusion and modular kernels at any irrational central charge
• On the Virasoro fusion kernel at $c=25$