Abstract
We show that if the one-loop partition function of a modular invariant conformal field theory can be expressed as a finite sum of holomorphically factorized terms thenc and all values ofh are rational.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Belavin, A., Polyakov, A., Zamolodchikov, A.: Infinite conformal symmetry in two-dimensional quantum field theory. Nucl. Phys.B241, 333 (1984)
Cardy, J.: Operator content of two-dimensional conformally invariant theories. Nucl. Phys.B270, 186 (1986)
Friedan, D., Shenker, S.: Lectures at IAS, 1987
Moore, G.: Nucl. Phys.B293, 139 (1987)
Kastor, D., Martinec, E., Qiu, Z.: Current algebra and conformal discrete series. Chicago preprint EFI-87-58
Dijkgraaf, R., Verlinde, E., Verlinde, H.: Conformal field theory atc=1. Utrecht preprints THU-87/17; THU-87/27
Friedan, D., Qiu, Z., Shenker, S. H.: Conformal invariance unitarity, and critical exponents in two dimensions. Phys. Rev. Lett.52, 1575 (1984)
Zamalodchikoc, A. B., Fateev, V. A.: Nonlocal (parafermion) currents in two-dimensional conformal quantum field theory and self-dual critical points inz N -symmetric statistical systems. JETP62, Disorder fields in two-dimensional conformal quantum-field theory andN=z extended supersymmetry. JETP63, 913 (1986)
Gepner, D., Qiu., Z.: Modular invariant partition functions for parafermionic field theories. Nucl. Phys.B285, 423 (1987)
Bagger, J., Nemeschansky, D., Yankielowicz, S.: Virasoro algebras with central chargec>1. Harvard preprint HUTP-87/A073
See, e.g. Gepner, D., Witten, E.: String theory on group manifolds. Nucl. Phys.B278, 493 (1986);
Bernard, D., Thierry-Mieg, J.: Bosonic Kac-Moody string theories. Phys. Lett.185B 65, (1986) and references therein
Ginsparg, P.: Curiosities atc=1 Harvard preprint. HUTP-87/A068
Friedan, D., Shenker, S.: The integrable analytic geometry of quantum string. Phys. Lett.175B, 287 (1986); The analytic geometry of two-dimensional conformal field theory. Nucl. Phys.B281, 509 (1987)
Ahlfors, L.: Complex analysis. New York: McGraw Hill 1966. See the last chapter
Deligne, P.: Equations différentielles à points singuliers réguliers. Lecture Notes in Mathematics, Vol. 163, Berlin, Heidelberg, New York: Springer 1970
Katz, N.: Publ. IHES,39, 355
Eguchi, T., Ooguri, H.: Differential equations for conformal characters in moduli space. Tokyo preprint
Kazhdan, D., Vafa, C.: unpublished
Herstein, I. N.: Topics in algebra Xerox, 1975
Lang, S.: Algebra. Reading, MA: Addison Wesley 1971
Harvey, J., Moore, G., Vafa, C.: Quasicrystalline compactification. PUPT-1068; IADDNS-HEP-87/48; HUTP-87/A072
Author information
Authors and Affiliations
Additional information
Communicated by L. Alvarez-Gaumé
Rights and permissions
About this article
Cite this article
Anderson, G., Moore, G. Rationality in conformal field theory. Commun.Math. Phys. 117, 441–450 (1988). https://doi.org/10.1007/BF01223375
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01223375