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The non-rational limit of D-series minimal models

by Sylvain Ribault

Submission summary

As Contributors: Sylvain Ribault
Arxiv Link:
Date submitted: 2020-03-10
Submitted by: Ribault, Sylvain
Submitted to: SciPost Physics Core
Discipline: Physics
Subject area: High-Energy Physics - Theory
Approach: Theoretical


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:
Editor-in-charge assigned

Author comments upon resubmission

According to the reviewer's report, some important subtleties in the article are not well explained. I have tried to clarify them.

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.

Submission & Refereeing History

Resubmission 1909.10784v2 on 10 March 2020
Submission 1909.10784v1 on 22 October 2019

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