A non-rational CFT with c=1 as a limit of minimal models

TL;DR

This paper explores the limit of minimal model conformal field theories as the central charge approaches one, proposing a new non-rational CFT that differs from free bosons and resembles Liouville theory, with explicit correlation functions and boundary states.

Contribution

It introduces a novel non-rational CFT at c=1 as a limit of minimal models, providing explicit correlation functions and boundary states, and supports its consistency.

Findings

Explicit three-point functions for bulk fields

Construction of conformal boundary states

Analytic and numerical evidence for a consistent CFT

Abstract

We investigate the limit of minimal model conformal field theories where the central charge approaches one. We conjecture that this limit is described by a non-rational CFT of central charge one. The limiting theory is different from the free boson but bears some resemblance to Liouville theory. Explicit expressions for the three point functions of bulk fields are presented, as well as a set of conformal boundary states. We provide analytic and numerical arguments in support of the claim that this data forms a consistent CFT.