Abstract
We initiate a program to study certain recent problems in non-compact coset CFT by the BRST approach. We derive a reduction formula for the BRST cohomology by making use of a twisting by highest weight modules. As illustrations, we apply the formula to the bosonic string model and a rank one non-compact coset model [DPL]. Our formula provides a completely new approach to non-compact coset construction.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
[FGZ] Frenkel, I. B., Garland, H., Zuckerman, G. J.: Semi-infinite cohomology and string theory. Proc. Natl. Acad. Sci. USA83, 8442 (1986)
[K1] Kac V. G.: Contravariant form for infinite-dimensional Lie algebras and superalgebras. Lecture Notes in Physics, Vol.94, p. 441. Berlin, Heidelberg, New York: Springer 1979
[K2] Kac, V. G.: Infinite dimensional Lie algebras. Cambridge: Cambridge University Press, 2nd Ed., 1985.
[Fe] Feigin, B. L.: The semi-infinite homology of Kac-Moody and Virasoro Lie algebras. Russ. Math. Surv.39, 155 (1984)
[LZ] Lian, B., Zuckerman, G. J.: BRST-cohomology of the Super Virasoro algebras, Commun. Math. Phys.125, 301–335 (1989)
[Zu] Zuckerman, G. J.: Modular forms, strings, and Ghosts. Proceedings of Symposia in Pure Math., Vol.49, Gunning R. Ehrenpreis L. (eds.) (1989), Part I pp. 273–284
[Le] Leites, D. A.: Cohomologies of Lie superalgebras. Funct. Anal. Appl.9, 340 (1975)
[HS] Hilton, P. J., Stammbach, U.: A course in Homological algebra, Berlin, Heidelberg, New York: Springer 1970, Chap. 7
[GSW] Green, M. B., Schwarz, J. H., Witten, E.: Superstring theory, Vol. 1, Cambridge: Cambridge University Press 1987
[GT] Goddard, P., Thorn, C. B.: Compatibility of the Dual Pomeron with Unitarity and Absence of Ghosts in the Dual Resonance Model, Phys. Lett.40B, 235–238 (1972)
[T1] Thorn, C. B.: Computing the Kac determinant using dual model techniques and more about the no-ghost theorem. Nucl. Phys.B248, 551 (1984)
[GW] Gepner, D., Witten, E.: String theory on Group manifolds, Nucl. Phys.B278, 493 (1986)
[G1] Gepner, D.: Spacetime supersymmetry in compactified string theory and superconformal models.' PUPT-1056 (1987)
[DPL] Dixon, L. J., Peskin, M. E., Lykken, J.:N=2 superconformal symmetry andSO(2,1) current Algebra. SLAC-PUB-4884 (1989)
[KK] Kac, V. G., Kazhdan, D. A.: Structure of representations with highest weights of infinite dimensional Lie algebras, Adv. Math.34, 97 (1979)
[W] Wallach, N. R.: On the unitarizability of derived functor modules. Invent. Math.78, 131–141 (1984)
[F] Farnsteiner, R.: Derivations and central extensions of Finitely Generated Lie Algebra, J. Alg.118, 33–45 (1988)
[BO] Bershadsky, M., Ooguri, H. HiddenSL(n) Symmetry in CFT, Commun. Math. Phys.126, 49–83 (1989)
[KS] Kazama, Y., Suzuki, H.: Tokyo preprints UT-KOMABA-88-8, 88-13
[FF] Frenkel, E., Feigin, B.: Moscow preprint April-89, May-89
[Ba] Itzhak Bars.: Heterotic superstring vacua in 4-D based on non-compact affine Current algebras. USC-90/HEP02
[KPZ] Knizhnik, V. G., Polyakov, A. M., Zamolodchikov, A. B.: Fractal structure of 2d-quantum gravity. Mod. Phys. Lett. A, Vol.3 8, 819–826 (1988)
[HPV] Horvath, Z., Palla, L., Vecsernyes, P.: BRS Cohomology and 2d gravity. ITP Budapest Report No. 468, 1989
Author information
Authors and Affiliations
Additional information
Communicated by A. Jaffe
Partially supported by NSF Grant DMS-8703581
Rights and permissions
About this article
Cite this article
Lian, B.H., Zuckerman, G.J. BRST cohomology and highest weight vectors. I. Commun.Math. Phys. 135, 547–580 (1991). https://doi.org/10.1007/BF02104121
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02104121