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On 2d CFTs that interpolate between minimal models

by Sylvain Ribault

This Submission thread is now published as SciPost Phys. 6, 075 (2019)

Submission summary

As Contributors: Sylvain Ribault
Arxiv Link: (pdf)
Date accepted: 2019-06-17
Date submitted: 2019-05-29 02:00
Submitted by: Ribault, Sylvain
Submitted to: SciPost Physics
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


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.

Ontology / Topics

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2d minimal models Central charge Conformal field theory (CFT)

Published as SciPost Phys. 6, 075 (2019)

Author comments upon resubmission

I am grateful to the reviewer for valuable suggestions. The reviewer's main suggestion was to make the article clearer and more self-contained, in particular by summarizing the results in the introduction.

I have therefore restructured the article: the new Introduction (Section 1) now includes material from the former Introduction, the former Summary and discussion (Section 6), and whatever in Section 2 was needed for understanding the results. I have also added a subsection 1.3 with a summary of results, which hopefully also clarifies the structure of the article. Section 6 has now disappeared, most of the material moved to Section 1, the specific example of a four-point function however moved to the end of Section 4.

Notice that the formula (1.8) is a new way of writing the spectrums of D-series minimal models,
without distinguishing two cases depending on the parity of $p$. I hope that this makes limits easier to figure out.

List of changes

Here I am answering the reviewer's numbered suggestions:

1. See my comments above.

2. The formula in question is now called (1.12) instead of (2.28). I have added a couple of sentences on the summation indexing.

3. The figure now has a caption, it is now on page 10 instead of page 8.

4. The plural momentums is less common than momenta but it is correct. For reasons to use regular plurals when possible, see my blog post:

5. The formatting of references is a matter for the journal. Let me however point out that I take the articles I cite from arXiv. I cannot in principle vouch for the correctness and relevance of journal versions if they exist.

Submission & Refereeing History

Published as SciPost Phys. 6, 075 (2019)

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Resubmission 1809.03722v3 on 29 May 2019

Reports on this Submission

Anonymous Report 1 on 2019-6-6 (Invited Report)


The author has complied with the suggested changes, so I recommend the paper for publication.

  • validity: -
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