Abstract
We analyze the chiral properties of (orbifold) conformal field theories which are obtained from a given conformal field theory by modding out by a finite symmetry group. For a class of orbifolds, we derive the fusion rules by studying the modular transformation properties of the one-loop characters. The results are illustrated with explicit calculations of toroidal andc=1 models.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Belavin, A.A., Polyakov, A.M., Zamolodchikov, A.B.: Nucl. Phys. B241, 333 (1984)
Friedan, D., Qiu, Z., Shenker, S.: Phys. Rev. Lett.52, 1575 (1984)
Cardy, J.L.: Nucl. Phys. B270, [FS16] 186 (1986)
Cappelli, A., Itzykson, C., Zuber, J.-B.: Nucl. Phys. B280 [FS18] 445 (1987); Commun. Math. Phys.113, 1 (1987); Gepner, D., Nucl. Phys. B287, 111 (1987)
Verlinde, E.: Nucl. Phys. B300, 360 (1988)
Vafa, C.: Phys. Lett.206 B, 421 (1988)
Rehren, K.-H., Schroer, B.: Einstein causality and Artin braids. Berlin-preprint (April 1988)
Mathur, S., Mukhi, S., Sen, A.: Differential equations for correlators and characters in arbitrary rational conformal field theories. Preprint TIFR/TH/88-32
Moore, G., Seiberg, N.: Phys. Lett212 B, 451 (1988)
Dijkgraaf, R., Verlinde, E.: Modular invariance and the fusion algebra. Nucl. Phys. [Proc. Suppl.]5B, 87 (1988)
Moore, G., Seiberg, N.: Naturality in conformal field theory. Preprint IASSNS-HEP/88/31
Moore, G., Seiberg, N.: Classical and quantum conformal field theory. Commun. Math. Phys.123, 177–254 (1989)
Witten, E.: Quantum field theory and the Jones polynomial. Commun. Math. Phys.121, 351–399 (1989)
Goddard, P., Kent, A., Olive, D.: Commun. Math. Phys.103, 105 (1986)
Dixon, L., Harvey, J.A., Vafa, C., Witten, E.: Nucl. Phys. B282, 620 (1985); Nucl. Phys. B274, 285 (1986)
Hamidi, S., Vafa, C.: Nucl. Phys. B279, 465 (1987)
Dixon, L., Friedan, D., Martinec, E., Shenker, S.: Nucl. Phys. B282, 13 (1987)
Vafa, C.: Nucl. Phys. B273, 592 (1986)
Frenkel, I. B., Lepowski, J., Meurman, A.: In Vertex operators in mathematics and physics. Publications of the Math. Sci. Res. Inst. No. 3. Berlin, Heidelberg, New York: Springer 1984
Dixon, L., Ginsparg, P., Harvey, J.: Beauty and the beast: superconformal symmetry in a monster module. Commun. Math. Phys.119, 221 (1988)
Friedan, D., Shenker, S.: Nucl. Phys. B 281, 509 (1987)
Vafa, C.: Phys. Lett.199 B, 195 (1987)
Narain, K.S., Sarmadi, M. H., Vafa, C.: Nucl. Phys. B288, 551 (1987)
See for example Gorenstein, D.: Finite groups. New York: Harper & Row 1968
Lusztig, G.: Leading coefficients of character values of hecke algebras. In the Arcata Conference on Representations of Finite Groups. Fong, P. (ed.), Proceedings of Symposia in Pure Mathematics, Vol. 47 (1987); Characters of reductive groups over a finite field. Ann. of Math. Studies, Vol. 107. Princeton University Press 1984
Freed, D., Vafa, C.: Commun. Math. Phys.110, 349 (1987)
Narain, K.S.: Phys. Lett.169 B, 41 (1986); Narain, K.S., Sarmadi, M.H., Witten, E.: Nucl. Phys. B279, 369 (1987)
Dijkgraaf, R., Verlinde, E., Verlinde, H.: Commun. Math. Phys.115, 649 (1988)
Ginsparg, P.: Nucl. Phys. B295 [FS21], 153 (1988)
Harris, G.: Nucl. Phys. B300 [FS22], 588 (1988)
Wakimoto, M., Yamada, H.: Lett. Math. Phys.7, 513 (1983)
Dijkgraaf, R., Verlinde, E., Verlinde, H.: Conformal field theory atc=1. To be published in the proceedings of the 1987 Cargèse Summer School on Nonperturbative Quantum Field Theory
Dijkgraaf, R., Verlinde, E., Verlinde, H.: In Proceedings of the 1987 Copenhagen Conference. Singapure: World Scientific 1988
Bais, F.A., Bouwknegt, P., Surridge, M., Schoutens, K.: Nucl. Phys. B304, 348; 371 (1988)
Author information
Authors and Affiliations
Additional information
Communicated by A. Jaffe
Rights and permissions
About this article
Cite this article
Dijkgraaf, R., Vafa, C., Verlinde, E. et al. The operator algebra of orbifold models. Commun.Math. Phys. 123, 485–526 (1989). https://doi.org/10.1007/BF01238812
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01238812