Representations of infinite-dimensional algebras and conformal field theory: from $N=2$ to $\widehat{sl}(2\vert1)$
Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 2, pp. 195-240 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We review a number of constructions, realized in bosonic and $N=2$ strings, whith relate the affine Lie algebra $\widehat{sl}(2)$, affine superalgebra $\widehat {sl}(2|1)$, and the superconformal $N=2$ algebra.
@article{TMF_1997_112_2_a1,
     author = {A. M. Semikhatov},
     title = {Representations of infinite-dimensional algebras and conformal field theory: from $N=2$ to $\widehat{sl}(2\vert1)$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {195--240},
     year = {1997},
     volume = {112},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1997_112_2_a1/}
}
TY  - JOUR
AU  - A. M. Semikhatov
TI  - Representations of infinite-dimensional algebras and conformal field theory: from $N=2$ to $\widehat{sl}(2\vert1)$
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1997
SP  - 195
EP  - 240
VL  - 112
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1997_112_2_a1/
LA  - ru
ID  - TMF_1997_112_2_a1
ER  - 
%0 Journal Article
%A A. M. Semikhatov
%T Representations of infinite-dimensional algebras and conformal field theory: from $N=2$ to $\widehat{sl}(2\vert1)$
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1997
%P 195-240
%V 112
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1997_112_2_a1/
%G ru
%F TMF_1997_112_2_a1
A. M. Semikhatov. Representations of infinite-dimensional algebras and conformal field theory: from $N=2$ to $\widehat{sl}(2\vert1)$. Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 2, pp. 195-240. http://geodesic.mathdoc.fr/item/TMF_1997_112_2_a1/

[1] V. G. Kač, D. A. Kazhdan, Adv. Math., 34 (1979), 97 | DOI | MR | Zbl

[2] F. G. Malikov, B. L. Feigin, D. B. Fuks, Funkts. analiz i ego prilozh., 20:2 (1986), 25 | MR | Zbl

[3] L. Benoit, Y. Saint-Aubin, Phys. Lett. B, 215 (1987), 517–522 ; Int. J. Mod. Phys. A, 7 (1992), 3023–3033 ; 9 (1994), 547–566 | DOI | MR | DOI | MR | DOI | MR | Zbl

[4] A. Kent, Phys. Lett. B, 273 (1991), 56–62 ; 278 (1992), 443–448 | DOI | MR | DOI | MR

[5] M. Bauer, P. di Francesco, C. Itzykson, J.-B. Zuber, Nucl. Phys. B, 362 (1991), 515–562 | DOI | MR | Zbl

[6] M. Bauer, N. Sochen, Commun. Math. Phys., 152 (1993), 127–160 | DOI | MR | Zbl

[7] A. Ch. Ganchev, V. B. Petkova, Phys. Lett. B, 293 (1992), 56–66 ; 318 (1993), 77–84 | DOI | MR | DOI | MR

[8] P. Bowcock, G. M. T. Watts, Phys. Lett. B, 297 (1992), 282–288 ; П. Бодкок, Г. Ваттс, ТМФ, 98:3 (1994), 350–356 | DOI | MR | MR

[9] G. M. T. Watts, Nucl. Phys. B, 407 (1993), 213–236 | DOI | MR | Zbl

[10] W. Boucher, D. Friedan, A. Kent, Phys. Lett. B, 172 (1986), 316 | DOI | MR | Zbl

[11] M. Dörrzapf, Commun. Math. Phys., 180 (1996), 195–232 | DOI | MR

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

[13] A. M. Semikhatov, Inverting the Hamiltonian Reduction in String Theory, Talk at the 28th Symposium on the Theory of Elementary Particles. Wendisch-Rietz, September 1994, E-print hep-th/9410109

[14] A. M. Semikhatov, Nucl. Phys. B, 478 (1996), 209 | DOI | MR | Zbl

[15] H. Awata, Y. Yamada, Mod. Phys. Lett. A, 7 (1992), 1185 | DOI | MR | Zbl

[16] B. Feigin, F. Malikov, Integral Intertwining Operators And Complex Powers Of Differential ($q$-Difference) Operators, Kyoto preprint, RIMS-894 | MR

[17] O. Andreev, Phys. Lett. B, 363 (1995), 166 | DOI | MR

[18] B. Gato-Rivera, A. M. Semikhatov, Phys. Lett. B, 293 (1992), 72 ; Б. Гато-Ривера, А. М. Семихатов, ТМФ, 95:2 (1993), 239 | DOI | MR | MR | Zbl

[19] B. Gato-Rivera, A. M. Semikhatov, Nucl. Phys. B, 408 (1993), 133 | DOI | MR | Zbl

[20] M. Bershadsky, W. Lerche, D. Nemeschansky, N. P. Warner, Nucl. Phys. B, 401 (1993), 304–347 | DOI | MR | Zbl

[21] M. Ademollo et al., Phys. Lett. B, 62 (1976), 105 | DOI

[22] N. Marcus, A Tour through $N=2$ strings, E-print hep-th/9211059

[23] E. S. Fradkin, A. A. Tseytlin, Phys. Lett. B, 106 (1981), 63 | DOI | MR

[24] H. Ooguri, C. Vafa, Nucl. Phys. B, 361 (1991), 469–518 | DOI | MR

[25] D. Kutasov, E. Martinec, New Principles for String/Membrane Unification, E-print hep-th/9602049 | MR

[26] E. Martinec, Geometrical Structures of M-Theory, EFI-96-29

[27] T. Eguchi, S. Hosono, S.-K. Yang, Commun. Math. Phys., 140 (1991), 159 | DOI | MR | Zbl

[28] W. Lerche, Phys. Lett. B, 252 (1990), 349 | DOI | MR

[29] A. Schwimmer, N. Seiberg, Phys. Lett. B, 184 (1987), 191 | DOI | MR

[30] M. Bershadsky, H. Ooguri, Phys. Lett. B, 229 (1989), 374 | DOI | MR

[31] K. Ito, H. Kanno, Mod. Phys. Lett. A, 9 (1994), 1377 | DOI | MR | Zbl

[32] A. M. Semikhatov, Mod. Phys. Lett. A, 9 (1994), 1867 | DOI | MR | Zbl

[33] A. M. Semikhatov, I. Yu. Tipunin, All Singular Vectors of the $N=2$ Superconformal Algebra via the Algebraic Continuation Approach, E-print hep-th/9604176 | MR

[34] A. M. Semikhatov, Verma Modules, Extremal Vectors, and Singular Vectors on the Non-Critical $N=2$ String Worldsheet, E-print hep-th/9610084

[35] B. L. Feigin, A. M. Semikhatov, I. Yu. Tipunin, Equivalence between Categories of Verma Modules over the Affine $\widehat{sl}(2)$ and $N=2$ Superconformal Algebras, E-print hep-th/9701043 | MR

[36] A. M. Semikhatov, I. Yu. Tipunin, The Complete Structure of Verma Modules over the $N=2$ Superconformal Algebra, E-print hep-th/9704111 | MR

[37] W. Lerche, C. Vafa, N. P. Warner, Nucl. Phys. B, 324 (1989), 427 | DOI | MR

[38] S. V. Ketov, O. Lechtenfeld, Phys. Lett. B, 353 (1995), 463–470 | DOI | MR

[39] A. V. Stoyanovskii, B. L. Feigin, Funkts. analiz i ego prilozh., 28:1 (1994), 68 | MR | Zbl

[40] A. M. Semikhatov, I. Yu. Tipunin, Int. J Mod. Phys. A, 11 (1996), 4597 | DOI | MR | Zbl

[41] P. Bowcock, A. Taormina, Representation theory of the affine Lie superalgebra $sl(2\,|\,1)$ at fractional level, E-print hep-th/9605220 | MR

[42] D. H. Friedan, E. J. Martinec, S. H. Shenker, Nucl. Phys. B, 271 (1986), 93 | DOI | MR

[43] P. Di Vecchia, J. L. Petersen, M. Yu, H. B. Zheng, Phys. Lett. B, 174 (1986), 280 | DOI | MR

[44] Y. Kazama, H. Suzuki, Nucl. Phys. B, 321 (1989), 232 | DOI | MR

[45] V. G. Kač, Infinite dimensional Lie algebras, Cambridge University Press, Cambridge, 1990 | MR