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Meromorphic cosets and the classification of three-character CFT

Das, Arpit; Gowdigere, Chethan N.; Mukhi, Sunil

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Mr Arpit Das
PGR Student Doctor of Philosophy

Chethan N. Gowdigere

Sunil Mukhi


We investigate the admissible vector-valued modular forms having three independent characters and vanishing Wronskian index and determine which ones correspond to genuine 2d conformal field theories. This is done by finding bilinear coset-type relations that pair them into meromorphic characters with central charges 8, 16, 24, 32 and 40. Such pairings allow us to identify some characters with definite CFTs and rule out others. As a key result we classify all unitary three-character CFT with vanishing Wronskian index, excluding c = 8, 16. The complete list has two infinite affine series Br,1, Dr,1 and 45 additional theories. As a by-product, at higher values of the total central charge we also find constraints on the existence or otherwise of meromorphic theories. We separately list several cases that potentially correspond to Intermediate Vertex Operator Algebras.


Das, A., Gowdigere, C. N., & Mukhi, S. (2023). Meromorphic cosets and the classification of three-character CFT. Journal of High Energy Physics, 2023(3), Article 23 (2023).

Journal Article Type Article
Acceptance Date Feb 16, 2023
Online Publication Date Mar 3, 2023
Publication Date 2023
Deposit Date Apr 18, 2023
Publicly Available Date Apr 18, 2023
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2023
Issue 3
Article Number 23 (2023)


Published Journal Article (Advance online version) (959 Kb)

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Copyright Statement
Advance online version This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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