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Meromorphic cosets and the classification of three-character CFT

  • Regular Article - Theoretical Physics
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  • Published: 03 March 2023
  • Volume 2023, article number 23, (2023)
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Journal of High Energy Physics Aims and scope Submit manuscript
Meromorphic cosets and the classification of three-character CFT
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  • Arpit Das  ORCID: orcid.org/0000-0003-4597-78461,
  • Chethan N. Gowdigere2,3 &
  • Sunil Mukhi  ORCID: orcid.org/0000-0001-9849-90704,5 

  • 224 Accesses

  • 6 Citations

  • 1 Altmetric

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A preprint version of the article is available at arXiv.

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.

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Authors and Affiliations

  1. Centre for Particle Theory, Department of Mathematical Sciences, Durham University, South Road, Durham, DH1 3LE, United Kingdom

    Arpit Das

  2. National Institute of Science Education and Research Bhubaneshwar, P.O. Jatni, Khurdha, 752050, India

    Chethan N. Gowdigere

  3. Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai, 400094, India

    Chethan N. Gowdigere

  4. School of Natural Sciences, Institute for Advanced Study, 1, Einstein Drive, Princeton, NJ, 08540, USA

    Sunil Mukhi

  5. Indian Institute of Science Education and Research, Homi Bhabha Rd, Pune, 411008, India

    Sunil Mukhi

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  1. Arpit Das
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Correspondence to Chethan N. Gowdigere.

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ArXiv ePrint: 2212.03136

Adjunct Professor, ICTS-TIFR, Bengaluru. (Sunil Mukhi)

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Das, A., Gowdigere, C.N. & Mukhi, S. Meromorphic cosets and the classification of three-character CFT. J. High Energ. Phys. 2023, 23 (2023). https://doi.org/10.1007/JHEP03(2023)023

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  • Received: 26 December 2022

  • Accepted: 16 February 2023

  • Published: 03 March 2023

  • DOI: https://doi.org/10.1007/JHEP03(2023)023

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Keywords

  • Conformal Field Models in String Theory
  • Scale and Conformal Symmetries
  • Conformal and W Symmetry
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