D-E classification of the local extensions of $SU_2$ current algebras
Teoretičeskaâ i matematičeskaâ fizika, Tome 92 (1992) no. 3, pp. 507-521 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A method is developed for constructing single valued rational 4-point functions of primary fields for $su_2$ conformal current algebra satisfying the Knizhnik–Zamolodchikov equation. For integer conformal dimensions $\Delta$ these rational solutions are proven to be in one-to-one correspondence with non-diagonal modular invariant partition functions of the D-even and E-even series of the ADE classification.
@article{TMF_1992_92_3_a12,
     author = {L. Michel and Ya. S. Stanev and I. T. Todorov},
     title = {D-E classification of the local extensions of $SU_2$ current algebras},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {507--521},
     year = {1992},
     volume = {92},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_92_3_a12/}
}
TY  - JOUR
AU  - L. Michel
AU  - Ya. S. Stanev
AU  - I. T. Todorov
TI  - D-E classification of the local extensions of $SU_2$ current algebras
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1992
SP  - 507
EP  - 521
VL  - 92
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1992_92_3_a12/
LA  - en
ID  - TMF_1992_92_3_a12
ER  - 
%0 Journal Article
%A L. Michel
%A Ya. S. Stanev
%A I. T. Todorov
%T D-E classification of the local extensions of $SU_2$ current algebras
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1992
%P 507-521
%V 92
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1992_92_3_a12/
%G en
%F TMF_1992_92_3_a12
L. Michel; Ya. S. Stanev; I. T. Todorov. D-E classification of the local extensions of $SU_2$ current algebras. Teoretičeskaâ i matematičeskaâ fizika, Tome 92 (1992) no. 3, pp. 507-521. http://geodesic.mathdoc.fr/item/TMF_1992_92_3_a12/

[1] Kastler D. (ed.), The Algebraic Theory of Superselection Sectors. Introduction and Recent Results, Proc. Convegno Int. Palermo, World Scientific, Singapore, 1990 ; Haag R., Local Quantum Physics. Fields, Particles, Algebras, Springer, Berlin, 1992 | MR | Zbl | MR | Zbl

[2] Buchholz D., Mack G., Todorov I. T., “Localized automorphisms of the ${\rm U}(1)$-current algebra on the circle: an instructive example”, The algebraic theory of superselection sectors (Palermo, 1989), World Sci. Publ., River Edge, NJ, 1990, 356–378 ; Buchholz D., Mack G., Paunov R. R., Todorov I. T., “An algebraic approach to the classification of local conformal field theories”, IX-th International Congress on Mathematical Physics (Swansea, 1988), Hilger, Bristol, 1989, 299–305 ; Nucl. Phys. B, 5 (1988), 20 | MR | MR | DOI | MR

[3] Mack G., “Introduction to conformal invariant quantum field theory in twop and more dimensions”, Nonperturbative Quantum Field Theory, eds. G.'t Hooft et al., Plenum Press, New York, 1988, 353–383 | DOI | MR

[4] Furlan P., Sotkov G. M., Todorov I. T., Riv. Nuovo Cim., 12:6 (1989), 1–202 | DOI | MR

[5] Buchholz D., Shultz-Mirbach H., Rev. Math. Phys., 2 (1990), 105 | DOI | MR | Zbl

[6] Cardy J. L., Nucl. Phys. B, 366 (1991), 403 ; Nucl. Phys. B, 275:17 (1986), 200 | DOI | MR | DOI | MR

[7] Capelli A., Itzykson C., Zuber J.-B., Nucl. Phys. B, 280:18 (1987), 445 | DOI | MR

[8] Seinberg N., Witten E., Nucl. Phys. B, 276 (1986), 272 | DOI | MR

[9] Nahm W., Int. J. Mod. Phys. A, 6 (1991), 2837 | DOI | MR | Zbl

[10] Bouwknegt P., Phys. Lett. B, 184 (1987), 369 | DOI | MR

[11] Schellekens A. N., Yankielowicz, Nucl. Phys. B, 327 (1989), 673 ; Phys. Lett. B, 227 (1989), 387 ; Int. J. Mod. Phys. A, 5 (1990), 2903 | DOI | MR | DOI | MR | DOI | MR | Zbl

[12] Knizhnik V. G., Zamolodchikov A., Nucl. Phys. B, 247 (1984), 83 | DOI | MR | Zbl

[13] Zamolodchikov A. B., Fateev V. A., Sov. J. Nucl. Phys., 43 (1986), 657

[14] Stanev Ya. S., Todorov I. T., Hadjiivanov L. K., Phys. Lett. B, 276 (1992), 87 | DOI | MR

[15] Belavin A. A., Polyakov I. T., Zamolodchikov A. B., Nucl. Phys. B, 241 (1984), 333 | DOI | MR | Zbl

[16] Michel L., “Invariants polynomiaux des groupes de symetrie moleculaire et cristallographique”, Group Theoretical Methods in Physics (Proc. of the Fifth Int. Colloquium), Academic Press, New York, 1977, 75–91 ; Jaric M. V., Michel L., Sharp R. T., “Zeros of covariant vector fields for the point groups: invariant formulation”, J. Physique, 45:1 (1984), 1–27 | DOI | MR | DOI | MR

[17] Chevalley C., Amer. J. Math., 77 (1955), 778 | DOI | MR | Zbl

[18] Michel L., “Covariant symmetric non-associative algebras on group representations”, Symmetry in Nature, v. II, Scuola Normale Superiore, Pisa, 1989, 537–5488

[19] Gepner D., Witten E., Nucl. Phys. B, 278 (1986), 493 | DOI | MR

[20] Furlan P., Stanev Ya. S., Todorov I. T., Lett. Math. Phys., 22 (1991), 307 | DOI | MR | Zbl

[21] Bauer M., Di Franscesco Ph., Itzykson C., Zuber J.-B., Nucl. Phys. B, 362 (1991), 515 | DOI | MR | Zbl

[22] Moore G., Seiberg N., Nucl. Phys. B, 313 (1989), 16 | DOI | MR