no. 4
Arithmetic features of rational conformal field theory
Annales de l'I.H.P. Physique théorique, Tome 63 (1995) no. 4, pp. 427-453 
@article{AIHPA_1995__63_4_427_0,
     author = {Todorov, Ivan T.},
     title = {Arithmetic features of rational conformal field theory},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {427--453},
     year = {1995},
     publisher = {Gauthier-Villars},
     volume = {63},
     number = {4},
     mrnumber = {1367146},
     zbl = {0852.17027},
     language = {en},
     url = {https://www.numdam.org/item/AIHPA_1995__63_4_427_0/}
}
TY  - JOUR
AU  - Todorov, Ivan T.
TI  - Arithmetic features of rational conformal field theory
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1995
SP  - 427
EP  - 453
VL  - 63
IS  - 4
PB  - Gauthier-Villars
UR  - https://www.numdam.org/item/AIHPA_1995__63_4_427_0/
LA  - en
ID  - AIHPA_1995__63_4_427_0
ER  - 
%0 Journal Article
%A Todorov, Ivan T.
%T Arithmetic features of rational conformal field theory
%J Annales de l'I.H.P. Physique théorique
%D 1995
%P 427-453
%V 63
%N 4
%I Gauthier-Villars
%U https://www.numdam.org/item/AIHPA_1995__63_4_427_0/
%G en
%F AIHPA_1995__63_4_427_0
Todorov, Ivan T. Arithmetic features of rational conformal field theory. Annales de l'I.H.P. Physique théorique, Tome 63 (1995) no. 4, pp. 427-453. https://www.numdam.org/item/AIHPA_1995__63_4_427_0/

[AGO87] J.R.C. Arcuri, J.F. Gomez and D. Olive, Conformal subalgebras and symmetric spaces, Nucl. Phys., Vol. B285, 1987, pp. 327-339. | MR

[BB87] F.A. Bais and P.G. Bouwknegt, A classification of subgroup truncations of the bosonic string, Nucl. Phys., Vol. B279, 1987, pp. 561-570. | MR

[Ber87] D. Bernard, String characters from Kac-Moody automorphisms, Nucl. Phys., Vol. B288, 1987, pp. 628-648. | MR

[BH89] F. Beukers and G. Heckman, Monodromy for the hypergeometric function nFn-1, Invent. Math., Vol. 95, 1989, pp. 325-354; F. Beukers, Differential Galois theory, in [Wald92], pp. 413-439. | Zbl | MR

[Bir74] J.S. Birman, Braids, Links and Mapping Class Groups, Ann. of Math. Studies, Vol. 82, Princeton Univ. Press, 1974. | MR

[BN87] P. Bouwknegt and W. Nahm, Realization of the exceptional modular invariant A1(1) partition functions, Phys. Lett., Vol. B184, 1987, pp. 359-362. | MR

[CIZ87] A. Cappelli, C. Itzykson and J.-B. Zuber, The A-D-E classification of minimal and A1(1) conformal invariant theories, Commun. Math. Phys., Vol. 113, 1987, pp. 1-26. | Zbl | MR

[Chr87] P. Christe, On exceptional operator algebras in the conformally invariant SU (2) Wess-Zumino-Witten model, Phys. Lett., Vol. 189B, 1987, pp. 215-220. | MR

[ChrF87] P. Christe and R. Flüme, The four point correlation functions of all primary fields of the d = 2 conformally invariant SU (2) σ-model with Wess-Zumino term, Nucl. Phys., Vol. B282, 1987, pp. 466-494. | MR

[CW92] P.B. Cohen and J. Wolfart, Algebraic Appell-Lauricella functions, Analysis, Vol. 12, 1992, pp. 359-376. | Zbl | MR

[CG94] A. Coste and T. Gannon, Galois symmetry in RCFT, Phys. Lett., Vol. B323, 1994, pp. 316-321.

[CM57] H.S.M. Coxeter and W.O.J. Moser, Generators and Relations for Discrete Groups, Springer, Berlin et al., 1957. | Zbl | MR

[deBG91] J. De Boer and J. Goeree, Markov traces and II1 factors in conformal field theory, Commun. Math. Phys., Vol. 139, 1991, pp. 267-304. | Zbl | MR

[DHR69] S. Doplicher, R. Haag and J.E. Roberts, Fields, observables and gauge transformations, I and II, Commun. Math. Phys., Vol. 13, 1969, pp. 1-23 and Vol. 15, 1969, pp.173-200; S. Doplicher and J.E. Roberts, Why there is a field algebra with a compact gauge group describing the superselection structure in particle physics, Commun. Math. Phys., Vol. 131, 1991, pp. 51- 107. | Zbl | MR

[DF84] Vl.S. Dotsenko and V.A. Fateev, Conformal algebra and multipoint correlation functions in 2D statistical models, Nucl. Phys., Vol. B240, 1984, pp. 312-348. | MR

[FFK89] G. Felder, J. Fröhlich and G. Keller, Braid matrices and structure constants for minimal conformal models, Commun. Math. Phys., Vol. 124, 1989, pp. 647-664. | Zbl | MR

[FGK88] G. Felder, K. Gawedzki and A. Kupiainen, Spectra of Wess-Zumino-Witten models with arbitrary simple groups, Commun. Math. Phys., Vol. 117, 1988, pp. 127-158; see also Nucl. Phys., Vol. B299, 1988, pp. 355-366. | Zbl | MR

[FG-RSS94] J. Fuchs, B. Gato-Rivera, B. Schellekens and Ch. Schweigert, Modular invariants and fusion rule automorphisms from Galois theory, Phys. Lett., Vol. B334, 1994, pp. 113-120. | MR

[FK89] J. Fuchs and A. Klemm, The computation of the operator algebra in non-diagonal conformal field theories, Ann. Phys. (N.Y.), Vol. 194, 1989, pp. 303-335. | Zbl | MR

[FK90] J. Fuchs, A. Klemm and C. Scheich, The operator algebra of the E8 type SU2 WZW theory, Zeitschr. f. Phys., Vol. C46, 1990, pp. 71-74.

[FSS94] J. Fuchs, B. Schellekens and Ch. Schweigert, Quasi-Galois symmetries of the modular S-matrix, Amsterdam preprint, NIKHEF-H/94-37, hep-th/94 12 009, Commun. Math. Phys. (to appear). | MR

[FST89] P. Furlan, G. Sotkov and I.T. Todorov, Two-dimensional conformal quantum field theory, Riv. Nuovo Cim., Vol. 12, 6, 1989, pp. 1-202. | MR

[FST91] P. Furlan, Ya. S. Stanev and I.T. Todorov, Coherent state operators and n-point invariants for Uq (sl(2)), Lett. Math. Phys., Vol. 22, 1991, pp. 307-319. | Zbl | MR

[Gan94] T. Gannon, The classification of su (m)k automorphism invariants, IHES, Bures-sur-Yvette, preprint, hep-th/94 08 119; T. Gannon, C. Jakovljevic and M.A. Walton, Lie group weight multiplicities from conformal field theory, Bures-sur-Yvette, preprint, IHES/P/94/58.

[G088] P. GODDARD and D. OLIVE (eds), Kac-Moody and Virasoro Algebras, A Reprint Volume for Physicists, World Scientific, Singapore, 1988. | Zbl | MR

[HPT91] L.K. Hadjiivanov, R.R. Paunov and I.T. Todorov, Quantum group extended chiral p-models, Nucl. Phys., Vol. B356, 1991, pp. 387-438. | MR

[Jones83] V. Jones, Braid groups, Hecke algebras and type II1 factors, in: Geometric Methods in Operator Algebras, Kyoto, 1983, Pitman Res. Notes in Math., Vol. 123, 1986, pp. 242-273. | Zbl | MR

[Kac85] V.G. Kac, Infinite-Dimensional Lie Algebras, Second edition (Cambridge Univ. Press, 1985); Third edition (ibid., 1990). | MR

[KW94] V.G. Kac and M. Wakimoto, Integrable highest weight modules over affine superalgebras and number theory, in: Lie Theory and Geometry, in Honor of Bertram Kostant, Progress in Mathematics, Vol. 123, Birkhäuser, Boston et al., 1994, pp. 415-456. | Zbl | MR

[KZ84] V.G. Knizhnik and A.B. Zamolodchikov, Current algebra and Wess-Zumino model in two dimensions, Nucl. Phys., Vol. B247, 1984, pp. 83-103. | Zbl | MR

[Mack88] G. Mack, Introduction to conformal invariant quantum field theory in two and more dimensions, in: Nonperturbative Quantum Field Theory, G.'t Hooft et al., eds. Plenum Press, N.Y., 1988, pp. 353-383. | MR

[MST92] L. Michel, Ya.S. Stanev and I.T. Todorov, D-E classification of the local extensions of the su2 current algebras, Teor. Mat. Fiz., Vol. 92, 1992, pp. 507- 521; Theor. Math. Phys., Vol. 92, 1993, p. 1063; Ya.S. Stanev and I.T. Todorov, Local 4-point functions and the Knizhnik-Zamolodchikov equation, in: Mathematical Aspects of Conformal and Topological Field Theories and Quantum Groups, P. J. SALLY Jr., M. FLATO, J. LEPOWSKY, N. RESHETIKHIN and G. J. ZUCKERMAN, eds., AMS-IMS-SIAM Summer Research Conference, June 1992, Mount Holyoke College, Contemporary Mathematics, Vol. 175, 1994, pp. 249-267. | Zbl | MR

[MS89] G. Moore and N. Seiberg, Classical and quantum conformal field theory, Commun. Math. Phys., Vol. 123, 1989, pp. 177-254. | Zbl | MR

[Pas87] V. Pasquier, Operator content of the A-D-E lattice models, J. Phys. A: Math. Gen., Vol. 120, 1987, pp. 5707-5717. | MR

[Pet89] V.B. Petkova, Structure constants of the (A, D) minimal c < 1 conformal models, Phys. Lett., Vol. 225, 1989, pp. 357-362.

[PZ95] V.B. Petkova and J.-B. Zuber, On structure constants of sl(2) theories, Nucl. Phys., Vol. B438, 1995, pp. 347-372. | Zbl | MR

[RS89] K.-H. Rehren and B. Schroer, Einstein causality and Artin braids, Nucl. Phys., Vol. B312, 1989, pp.715-750. | MR

[RST94] K.-H. Rehren, Y.S. Stanev and I.T. Todorov, Characterizing invariants for local extensions of current algebras, Hamburg-Vienna preprint DESY 94-164, ESI 132, 1994, hep-th/94 09 165; Commun. Math. Phys. | MR

[RTW93] Ph. Ruelle, E. Thirran and J. Weyers, Implications of an arithmetical symmetry of the commutant for modular invariants, Nucl. Phys., Vol. B402, 1993, pp. 693-708. | Zbl | MR

[SST95] H. Sazdjian, Ya.S. Stanev and I.T. Todorov, SU3 coherent state operators and invariant correlation functions and their quantum group counterparts, J. Math. Phys., Vol. 36, 1995, pp. 2030-2052. | Zbl | MR

[SW86] A.N. Schellekens and N.P. Warner, Conformal subalgebras of Kac-Moody algebras, Phys. Rev., Vol. D34, 1986, pp. 3092-3101. | MR

[SY89] A.N. Schellekens and S. Yankielowicz, Extended chiral algebras and modular invariant partition functions, Nucl. Phys., Vol. B327, 1989, pp. 673-703; Simple currents, modular invariants and fixed points, Int. J. Mod. Phys., Vol. A5, 1990, pp. 2903-2952. | MR

[Sch74] B. Schroer, A trip to scalingland, Proceedings of the V Brazilian Symposium on Theoretical Physics, Rio de Janeiro, Jan. 1974, ed. by E. FERREIRA (Livros Tecnios e Cientificos Editora S.A., Rio de Janeiro, 1975).

[Sch1873] H.A. Schwarz, Über diejenigen Fälle in welhen die Gaußische hypergeometrische Reihe eine algebraische Funktion ihres vierten Elements darstelt, Reine Angew. Math. (Crelle J.), Vol. 75, 1873, pp. 292-335. | JFM

[Slo83] P. Slodowy, Platonic solids, Kleinian singularities and Lie groups, Lect. Notes in Math., Vol. 1008, Springer, Berlin, 1983, pp. 102-138. | Zbl | MR

[ST94] Ya.S. Stanev and I.T. Todorov, On Schwarz problem for the sû2 Knizhnik-Zamolodchikov equation, Vienna preprint, ESI 121, 1994; Lett. Math. Phys., Vol. 35, 1995, pp. 123-134. | Zbl | MR

[ST95] Ya.S. Stanev and I.T. Todorov, Monodromy representations of the mapping class group Bn for the su2 Knizhnik-Zamolodchikov equation, 1995, Schladming lecture, Vienna preprint, ESI 233, 1995. | MR

[STH92] Ya.S. Stanev and I.T. Todorov, L.K. Hadjiivanov, Braid invariant rational conformal models with a quantum group symmetry, Phys. Lett., Vol. B276, 1992, pp. 87-94; and in: Quantum Symmetries, H.-D. DOEBNER and V. K. DOBREV eds., World Scientific, Singapore, 1993, pp. 24-40. | MR

[Tod94] I.T. Todorov, What are we learning from 2-dimensional conformal models? in: Mathematical Physics Towards the 21st Century, R. N. SEN and A. GERSTEN, eds., Ben-Gurion University of the Negev Press, 1994, pp. 160-176.

[TK88] A. Tsuchiya and Y. Kanie, Vertex operators in the conformal field theory on P1 and monodromy representations of the braid group, in: Conformal Field Theory and Solvable Lattice Models, Advanced Studies in Pure Mathematics, Vol. 16, 1988, pp. 297-372; Lett. Math. Phys., Vol. 13, 1987, pp. 303-312. | Zbl | MR

[Wald92] M. Waldschmidt et al., (eds.), From Number Theory to Physics, Springer, Berlin, 1992. | Zbl | MR

[ZF86] A.B. Zamolodchikov and V.A. Fateev, Operator algebra and correlation functions in the two-dimensional SU (2) x SU (2) chiral Wess-Zumino model, Yad. Fiz., Vol. 43, 1986, pp. 1031-1044 (transl: Sov. J. Nucl. Phys., Vol. 43, 1986, pp. 657-664).