Cosets of meromorphic CFTs and modular differential equations

  • Matthias R. Gaberdiel
  • Harsha R. Hampapura
  • Sunil Mukhi
Open Access
Regular Article - Theoretical Physics


Some relations between families of two-character CFTs are explained using a slightly generalised coset construction, and the underlying theories (whose existence was only conjectured based on the modular differential equation) are constructed. The same method also gives rise to interesting new examples of CFTs with three and four characters.


Conformal and W Symmetry Field Theories in Lower Dimensions 


Open Access

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.


  1. [1]
    S.D. Mathur, S. Mukhi and A. Sen, On the classification of rational conformal field theories, Phys. Lett. B 213 (1988) 303 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    S.D. Mathur, S. Mukhi and A. Sen, Reconstruction of conformal field theories from modular geometry on the torus, Nucl. Phys. B 318 (1989) 483 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    S.G. Naculich, Differential equations for rational conformal characters, Nucl. Phys. B 323 (1989) 423 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    H.R. Hampapura and S. Mukhi, On 2d conformal field theories with two characters, JHEP 01 (2016) 005 [arXiv:1510.04478] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    P. Goddard, A. Kent and D.I. Olive, Unitary representations of the Virasoro and super-Virasoro algebras, Commun. Math. Phys. 103 (1986) 105 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    C. Dong and G. Mason, Coset constructions and dual pairs for vertex operator algebras, math/9904155.
  7. [7]
    H. Li, On Abelian coset generalized vertex algebras, submitted to Commun. Contemp. Math. (2000) [math/0008062] [INSPIRE].
  8. [8]
    A.N. Schellekens, Meromorphic c = 24 conformal field theories, Commun. Math. Phys. 153 (1993) 159 [hep-th/9205072] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    P.S. Montague, Orbifold constructions and the classification of selfdual c = 24 conformal field theories, Nucl. Phys. B 428 (1994) 233 [hep-th/9403088] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    C.H. Lam and H. Shimakura, Classification of holomorphic framed vertex operator algebras of central charge 24, Amer. J. Math. 137 (2015) 111 [arXiv:1209.4677].MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Matthias R. Gaberdiel
    • 1
  • Harsha R. Hampapura
    • 2
  • Sunil Mukhi
    • 2
  1. 1.Institut für Theoretische PhysikETH ZürichZürichSwitzerland
  2. 2.Indian Institute of Science Education and ResearchPuneIndia

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