Free-field resolutions of unitary representations of the $N=2$ Virasoro algebra: I
Teoretičeskaâ i matematičeskaâ fizika, Tome 121 (1999) no. 1, pp. 89-109 Cet article a éte moissonné depuis la source Math-Net.Ru

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We construct a free-field resolution of unitary representations of the $N=2$ superconformal algebra. The resolution is degenerated by the action of one fermionic screening operator (which generates the “gravitational descendants” in the field theory picture). The irreducible representation is singled out from the free-field space as the cohomology of this screening operator.
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A. M. Semikhatov. Free-field resolutions of unitary representations of the $N=2$ Virasoro algebra: I. Teoretičeskaâ i matematičeskaâ fizika, Tome 121 (1999) no. 1, pp. 89-109. http://geodesic.mathdoc.fr/item/TMF_1999_121_1_a5/

[1] B. L. Feigin, D. B. Fuchs, “Representations of the Virasoro Algebra”, Representations of Lie Groups and Related Topics, eds. A. A. Vershik and D. A. Zhelobenko, Gordon and Breach, N. Y., 1990 | MR

[2] G. Felder, Nucl. Phys. B, 317 (1989), 215 ; 324, 548 | DOI | MR | MR

[3] I. Bernshtein, I. Gelfand, S. Gelfand, Funk. An. Prilozh., 10 (1976), 1 | DOI | Zbl

[4] D. Bernard, G. Felder, Commun. Math. Phys., 127 (1990), 145 | DOI | MR | Zbl

[5] B. L. Feigin, E. V. Frenkel, “Representations of Affine Kac–Moody Algebras and Bosonization”, Physics and Mathematics of Strings, Memorial Volume for Vadim Knizhnik, eds. L. Brink, D. Friedan, A. M. Polyakov, World Sci. ; Commun. Math. Phys., 128 (1990), 161 | MR | DOI | MR | Zbl

[6] P. Bouwknegt, J. McCarthy, K. Pilch, Commun. Math. Phys., 131 (1990), 125 | DOI | MR | Zbl

[7] B. L. Feigin, A. M. Semikhatov, V. A. Sirota, I. Yu. Tipunin, Nucl. Phys. B, 536 (1999), 617 ; E-print hep-th/9805179 | DOI | MR | Zbl

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

[9] P. Fré, L. Girardello, A. Lerda, P. Soriani, Nucl. Phys. B, 387 (1992), 333 | DOI | MR

[10] E. Witten, Int. J. Mod. Phys. A, 9 (1994), 4783 | DOI | MR | Zbl

[11] T. Kawai, Y. Yamada, S.-K. Yang, Nucl. Phys. B, 414 (1994), 191 | DOI | MR | Zbl

[12] D. Nemeschansky, N. P. Warner, Nucl. Phys. B, 442 (1995), 623 | DOI | MR | Zbl

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

[14] B. L. Feigin, A. M. Semikhatov, I. Yu. Tipunin, Equivalence between Chain Categories of Representations of Affine $s\ell(2)$ and $N=2$ Superconformal Algebras, ; J. Math. Phys., 39 (1998), 3865 E-print hep-th/9701043 | MR | DOI | Zbl

[15] A. M. Semikhatov, I. Yu. Tipunin, Commun. Math. Phys., 195 (1998), 129 | DOI | MR | Zbl

[16] A. S. Lossev (Losev), Descendants Constructed from Matter Field and K. Saito Higher Residue Pairing in Landau–Ginzburg Theories Coupled to Topological Gravity, E-print hep-th/9211090 | MR

[17] T. Eguchi, H. Kanno, Y. Yamada, S.-K. Yang, Phys. Lett. B, 305 (1993), 235 | DOI | MR

[18] W. Lerche, N. P. Warner, Phys. Lett. B, 343 (1995), 87 | DOI | MR

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

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

[21] E. Verlinde, H. Verlinde, Nucl. Phys. B, 348 (1991), 457 ; R. Dijkgraaf, E. Verlinde, H. Verlinde, Notes on Topological String Theory and $2d$ Quantum Gravity, PUPT-1217, Princeton Univ., Princeton, 1990 | DOI | MR | MR

[22] K. Landsteiner, W. Lerche, A. Sevrin, Phys. Lett. B, 352 (1995), 286 | DOI | MR

[23] W. Lerche, Nucl. Phys. B, 434 (1995), 445 ; Chiral Rings and Integrable Systems for Models of Topological Gravity, E-print hep-th/9401121 | DOI | MR | Zbl

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

[25] R. Dijkgraaf, E. Verlinde, H. Verlinde, Nucl. Phys. B, 352 (1991), 59 | DOI | MR

[26] A. M. Semikhatov, B. L. Feigin, TMF, 121:2 (1999), 244–257 (to appear) | DOI | MR | Zbl

[27] 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