Modules de plus haut poids unitarisables sur la super-algèbre de Virasoro N=2 tordue
Iohara, Kenji
Annales de l'Institut Fourier, Tome 58 (2008), p. 733-754 / Harvested from Numdam

Dans cet article, on classifie les modules de plus haut poids unitarisables sur la super-algèbre de Virasoro N=2 tordue.

In this article, we classify the unitarizable highest weight modules over the twisted sector of the N=2 super Virasoro algebra.

Publié le : 2008-01-01
DOI : https://doi.org/10.5802/aif.2367
Classification:  17B10,  17B68
Mots clés: super-algèbre de Virasoro N=2 tordue, modules uintarisables, parafermion
@article{AIF_2008__58_3_733_0,
     author = {Iohara, Kenji},
     title = {Modules de plus haut poids unitarisables sur la super-alg\`ebre de Virasoro $N=2$ tordue},
     journal = {Annales de l'Institut Fourier},
     volume = {58},
     year = {2008},
     pages = {733-754},
     doi = {10.5802/aif.2367},
     zbl = {1174.17021},
     mrnumber = {2427508},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIF_2008__58_3_733_0}
}
Iohara, Kenji. Modules de plus haut poids unitarisables sur la super-algèbre de Virasoro $N=2$ tordue. Annales de l'Institut Fourier, Tome 58 (2008) pp. 733-754. doi : 10.5802/aif.2367. http://gdmltest.u-ga.fr/item/AIF_2008__58_3_733_0/

[1] Boucher, W.; Friedan, D.; Kent, A. Determinant Formulae and Unitarity for the N=2 Superconformal Algebras in Two Dimensions or Exact Results on String Compactification, Phys. Lett. B, Tome 172 (1986), pp. 316-322 | Article | MR 844506 | Zbl 1174.81319

[2] Chari, V.; Pressley, A. Unitary representations of the Virasoro algebra and a conjecture of Kac, Compos. Math., Tome 67 (1988), pp. 315-342 | Numdam | MR 959215 | Zbl 0661.17022

[3] Friedan, D.; Qiu, Z.; Shenker, S. Conformal Invariance, Unitarity, and Critical Exponents in Two Dimensions, Phys. Rev. Lett., Tome 52 (1984), pp. 1575-1578 | Article | MR 740343

[4] Friedan, D.; Qiu, Z.; Shenker, S. Superconformal Invariance in Two Dimensions and Tricritical Ising Model, Phys. Lett. B, Tome 151 (1985), pp. 37-43 | Article | MR 778509

[5] Goddard, P.; Kent, A.; Olive, D. Unitary Representations of the Virasoro and Super-Virasoro Algebras, Comm. Math. Phys., Tome 103 (1986), pp. 105-119 | Article | MR 826859 | Zbl 0588.17014

[6] Iohara, K.; Koga, Y. Representation theory of N=2 super Virasoro algebra : twisted sector, Jour. Funct. Anal., Tome 214 (2004), pp. 450-518 | Article | MR 2083310 | Zbl pre02105320

[7] Kac, V. G. Infinite dimensional Lie algebras, Cambr. Univ. Press (1991) | MR 1104219 | Zbl 0716.17022

[8] Langlands, R. P.; Kass, S. On unitary representations of the Virasoro algebra, Infinite dimensional Lie algebras and their applications, Singapore, World Scientific (1988) | MR 1114998 | Zbl 0748.17025

[9] Lepowsky, J.; Wilson, R. L. A new family of algebras underlying the Rogers-Ramanujan identities and generalizations, Proc. Natl. Acad. Sci., USA, Tome 78 (1981), pp. 7254-7258 | Article | MR 638674 | Zbl 0472.17005

[10] Rittenberg, V.; Schwimmer, A. A Connection between the Twisted N=2 Superconformal and SU(2) Kac-Moody Algebras, Phys. Lett. B, Tome 195 (1987), pp. 135-138 | Article | MR 910255

[11] Sauvageot, F. Représentations unitaires des super-algèbres de Ramond et de Neveu-Schwartz, Comm. Math. Phys., Tome 121 (1989), pp. 639-657 | Article | MR 990996 | Zbl 0676.17017

[12] Zamolodchikov, A. B.; Fateev, V. A. Disorder fields in two-dimensional conformal quantum-field theory and N=2 extended supersymmetry, Zh. Eksp. Teor. Fiz., Tome 90 (1986), pp. 1553-1566