Abstract
Using the method of modular-invariant differential equations, we classify a family of Rational Conformal Field Theories with two and three characters having no Kac-Moody algebra. In addition to unitary and non-unitary minimal models, we find “dual” theories whose characters obey bilinear relations with those of the minimal models to give the Moonshine Module. In some ways this relation is analogous to cosets of meromorphic CFT’s. The theory dual in this sense to the Ising model has central charge \( \frac{47}{2} \) and is related to the Baby Monster Module.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. Di Francesco, P. Mathieu and D. Senechal, Conformal Field Theory, Graduate Texts in Contemporary Physics, Springer-Verlag, New York U.S.A. (1997).
J.D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity, Commun. Math. Phys. 104 (1986) 207 [INSPIRE].
P. Goddard, A. Kent and D.I. Olive, Virasoro Algebras and Coset Space Models, Phys. Lett. B 152 (1985) 88 [INSPIRE].
P. Goddard, A. Kent and D.I. Olive, Unitary Representations of the Virasoro and Supervirasoro Algebras, Commun. Math. Phys. 103 (1986) 105 [INSPIRE].
A.A. Belavin, A.M. Polyakov and A.B. Zamolodchikov, Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory, Nucl. Phys. B 241 (1984) 333 [INSPIRE].
G.E. Andrews, R.J. Baxter and P.J. Forrester, Eight vertex SOS model and generalized Rogers-Ramanujan type identities, J. Statist. Phys. 35 (1984) 193 [INSPIRE].
I. Frenkel, J. Lepowsky and A. Meurman, Vertex Operator Algebras and the Monster, Academic Press, Boston U.S.A. (1988).
G. Anderson and G.W. Moore, Rationality in Conformal Field Theory, Commun. Math. Phys. 117 (1988) 441 [INSPIRE].
T. Eguchi and H. Ooguri, Differential Equations for Characters of Virasoro and Affine Lie Algebras, Nucl. Phys. B 313 (1989) 492 [INSPIRE].
S.D. Mathur, S. Mukhi and A. Sen, Differential Equations for Correlators and Characters in Arbitrary Rational Conformal Field Theories, Nucl. Phys. B 312 (1989) 15 [INSPIRE].
S.D. Mathur, S. Mukhi and A. Sen, On the Classification of Rational Conformal Field Theories, Phys. Lett. B 213 (1988) 303 [INSPIRE].
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].
H.R. Hampapura and S. Mukhi, On 2d Conformal Field Theories with Two Characters, JHEP 01 (2016) 005 [arXiv:1510.04478] [INSPIRE].
M.R. Gaberdiel, H.R. Hampapura and S. Mukhi, Cosets of Meromorphic CFTs and Modular Differential Equations, JHEP 04 (2016) 156 [arXiv:1602.01022] [INSPIRE].
G. Hoehn, Selbstduale Vertexoperatorsuperalgebren und das Babymonster (Self-dual Vertex Operator Super Algebras and the Baby Monster), arXiv:0706.0236.
S.G. Naculich, Differential equations for rational conformal characters, Nucl. Phys. B 323 (1989) 423 [INSPIRE].
A.N. Schellekens, Meromorphic C = 24 conformal field theories, Commun. Math. Phys. 153 (1993) 159 [hep-th/9205072] [INSPIRE].
G. Hoehn, Generalized Moonshine for the Baby Monster, https://www.math.ksu.edu/∼gerald/papers/baby8.ps
C. Dong, G. Mason and Y. Zhu, Discrete Series of the Virasoro Algebra and the Moonshine Module, Proc. Sympos. Pure Math. 56 (1994) 295 [http://www.ams.org/mathscinet-getitem?mr=1278737].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1605.03314
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Hampapura, H.R., Mukhi, S. Two-dimensional RCFT’s without Kac-Moody symmetry. J. High Energ. Phys. 2016, 138 (2016). https://doi.org/10.1007/JHEP07(2016)138
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2016)138