The non-rational limit of D-series minimal models

TL;DR

This paper investigates the limit of D-series minimal models as their central charge approaches an irrational value, revealing a non-rational, non-diagonal conformal field theory with unique structure constants.

Contribution

It introduces a new non-rational limit theory of D-series minimal models, highlighting differences from Liouville theory and analyzing correlation functions involving diagonal and non-diagonal fields.

Findings

Limit theory's structure constant differs from Liouville theory by a distribution factor.

Correlation functions involving diagonal and non-diagonal fields are smooth functions of conformal dimensions.

The limit theory exemplifies a non-diagonal, non-rational, exactly solved 2D CFT.

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.