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Curiosities above c = 24

by A. Ramesh Chandra, Sunil Mukhi

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Submission summary

Authors (as registered SciPost users): A. Ramesh Chandra · Sunil Mukhi
Submission information
Preprint Link: https://arxiv.org/abs/1812.05109v3  (pdf)
Date accepted: 2019-04-24
Date submitted: 2019-04-04 02:00
Submitted by: Mukhi, Sunil
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical

Abstract

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 $\ell=2$.

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.

Published as SciPost Phys. 6, 053 (2019)


Reports on this Submission

Report #1 by Anonymous (Referee 1) on 2019-4-12 (Invited Report)

Report

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

  • validity: -
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  • originality: -
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