## SciPost Submission Page

# The non-rational limit of D-series minimal models

### by Sylvain Ribault

### Submission summary

As Contributors: | Sylvain Ribault |

Arxiv Link: | https://arxiv.org/abs/1909.10784v2 |

Date submitted: | 2020-03-10 |

Submitted by: | Ribault, Sylvain |

Submitted to: | SciPost Physics Core |

Discipline: | Physics |

Subject area: | High-Energy Physics - Theory |

Approach: | Theoretical |

### 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.

###### Current status:

### Author comments upon resubmission

### List of changes

In response to the reviewer's suggestions:

1. I have written further explanations on the non-diagonal sector, and related it to the model's $\mathbb{Z}_2$ symmetry as discussed in Ref. [10]. See page 5 after Eq. (2.8), and page 6 the beginning of the last paragraph.

2. Writing that the limit of D-series minimal models was expected to be a diagonal extension of Liouville theory was actually an understatement of the major surprise that occurred. I have tried to explain this in more detail at the beginning of the Conclusion.

3. The role of the degenerate fields is now elaborated in more detail at the beginning of Section 2.2 (second paragraph).

4. The lack of symmetry under $\beta \to \frac{1}{\beta}$ is now demonstrated after Eq. (2.13).

Additional changes:

5. In the Conclusion (Outlook part), I have added a paragraph on possible generalizations.