On 2d CFTs that interpolate between minimal models

TL;DR

This paper explores exactly solvable 2D conformal field theories that interpolate between minimal models, analyzing their correlation functions and the behavior at rational central charges, revealing diverse limiting behaviors.

Contribution

It introduces a class of solvable 2D CFTs that interpolate between minimal models and analyzes their correlation functions at rational central charges.

Findings

Correlation functions tend to minimal models or diverge at rational central charges.

Correlation functions can have finite or logarithmic limits.

Analytic relations between structure constants and conformal blocks are established.

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.