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Curiosities above c = 24

by A. Ramesh Chandra, Sunil Mukhi

Submission summary

As Contributors: A. Ramesh Chandra · Sunil Mukhi
Arxiv Link: (pdf)
Date accepted: 2019-04-24
Date submitted: 2019-04-04 02:00
Submitted by: Mukhi, Sunil
Submitted to: SciPost Physics
Academic field: Physics
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical


Two-dimensional rational CFT are characterised by an integer $\ell$, related to the number of zeroes of the Wronskian of the characters. For two-character RCFT's with $\ell<6$ there is a finite number of theories and most of these are classified. Recently it has been shown that for $\ell \ge 6$ there are infinitely many admissible characters that could potentially describe CFT's. In this note we examine the $\ell=6$ case, whose central charges lie between 24 and 32, and propose a classification method based on cosets of meromorphic CFT's. We illustrate the method using theories on Kervaire lattices with complete root systems. In the process we construct the first known two-character RCFT's beyond $\ell=2$.

Ontology / Topics

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Conformal field theory (CFT)

Published as SciPost Phys. 6, 053 (2019)

Author comments upon resubmission

We have revised the article to incorporate the suggestions of both referees and the editor, notably by adding some introductory material and clarifying a few points.

List of changes

1. Explained that LY stands for "Lee-Yang"
2. Noted that at c=24, the number 71 of theories is subject to a uniqueness conjecture about the Monster CFT.
3. Added supplementary material in Sections 1 and 2 which address all the queries/comments of Referee 2 as well as the Editor's request to make the paper more self-contained.

Reports on this Submission

Anonymous Report 1 on 2019-4-12 (Invited Report)


The authors implemented the changes that I suggested in my previous report. I recommend the latest version of the article for publication.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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