Meromorphic cosets and the classification of three-character CFT

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

Abstract

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.

Citation

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). https://doi.org/10.1007/jhep03%282023%29023

• 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)
• DOI: https://doi.org/10.1007/jhep03%282023%29023