Curiosities above c = 24

Submission summary

 As Contributors: A. Ramesh Chandra · Sunil Mukhi Arxiv Link: https://arxiv.org/abs/1812.05109v3 Date accepted: 2019-04-24 Date submitted: 2019-04-04 Submitted by: Mukhi, Sunil Submitted to: SciPost Physics Domain(s): Theoretical Subject area: High-Energy Physics - Theory

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 $\ell=2$.

Current status:
Publication decision taken: accept

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.

Submission & Refereeing History

Resubmission 1812.05109v3 on 4 April 2019
Submission 1812.05109v2 on 31 January 2019

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

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