Affine orbifolds and rational conformal field theory extensions of W1+∞

Communications in Mathematical Physics

Volumn 190, Issue 1, 1997, Pages 57-111

  Kac, Victor G ^a   Todorov, Ivan T ^a,b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b INSTITUTE FOR NUCLEAR RESEARCH AND NUCLEAR ENERGY   (Bulgaria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002844269     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050234     Document Type: Article

References (46)

1. 1+∞ algebra. Prog. Theor. Phys., Proc. Suppl.118, 343-373 (1995)
2. 1+∞. New Trends in Quantum Field Theory In: Proc. of the 1995 Razlog (Bulgaria) Workshop, A. Ganchev et al. (eds.), Sofia: Heron Press, 1996 pp. 147-158
3. Belavin, A.A., Polyakov, A.M., Zamolodchikov, A.B.: Infinite conformal symmetry in two-dimensional quantum field theory. Nucl. Phys. B241, 333-381 (1984)
4. Borcherds, R.: Vertex algebras, Kac-Moody algebras and the Monster. Proc. Natl. Acad. Sci. USA 83, 3068-3071 (1986); Monstrous moonshine and monstrous Lie Superalgebras. Invent. Math. 109, 405-444 (1992)
5. Borcherds, R.: Vertex algebras, Kac-Moody algebras and the Monster. Proc. Natl. Acad. Sci. USA 83, 3068-3071 (1986); Monstrous moonshine and monstrous Lie Superalgebras. Invent. Math. 109, 405-444 (1992)
6. Bouwknegt, P., McCarthy, J., Pilch, K.: Semi-infinite cohomology and w-gravity. J. Geom. Phys. 11, 225-249 (1993)
7. Buchholz, D., Mack, G., Todorov, I.T.: The current algebra on the circle as a germ of local field theory. Nucl. Phys. B (Proc. Suppl.) 5B, 20-56 (1988)
8. 1+∞ dynamics of edge excitations in the quantum Hall effect, Ann. Phys. (NY) 246, 86-120 (1996)
9. 1+∞ dynamics of edge excitations in the quantum Hall effect, Ann. Phys. (NY) 246, 86-120 (1996)
10. Cappelli, A., Zemba, G.: Modular invariant partition functions in the quantum Hall effect. hep-th/9605127
11. Di Francesco, P., Saleur, H., Zuber, J.-B.: Modular invariance in non-minimal two-dimensional conformal theories. Nucl. Phys. B285, [FS19] 454-480 (1987)
12. Dijkgraaf, R., Vafa, C., Verlinde, E., Verlinde, H.: The operator algebra of orbifold models. Commun. Math. Phys. 123, 485-526 (1989)
13. Dolan, L., Goddard, P., Montague, P.: Conformal field theory of twisted vertex operators. Nucl. Phys. B338, 529-601 (1990)
14. 3 and their application to the elementary particle spectrum. J. Math. Phys. 5, 1038-1051 (1964)
15. Flohr, M.: W-algebras, new rational models and completeness of the c = 1 classification. Commun. Math. Phys. 157, 179-212 (1993)
16. Frenkel, I.B., Kac, V.G.: Basic representations of affine Lie algebras and dual resonance models. Invent. Math. 62, 23-66 (1980)
17. N) with central charge N. Commun. Math. Phys. 170, 337-357 (1995)
18. Frenkel, E., Kac, V., Wakimoto, M.: Characters and fusion rules for W-algebra via quantized Drinfield-Sokolov reduction. Commun. Math. Phys. 147, 295-328 (1992)
19. Frenkel, I.B., Lepowsky, J., Meurman, A.: Vertex Operator Algebras and the Monster. New York: Academic Press, 1988
20. Frenkel, I.B., Zhu, Y.: Vertex operator algebras associated to representations of affine and Virasoro algebra. Duke Math. J. 66, 123-168 (1992)
21. Fröhlich, J., Thiran, E.: Integral quadratic forms, Kac-Moody algebras, and fractional quantum Hall effect. An ADE-O classification. J. Stat. Phys. 76, 209-283 (1994)
22. Furlan, P., Sotkov, G.M., Todorov, I.T.: Two-dimensional conformal quantum field theory. Riv. Nuovo Gim 12:6, 1-202 (1989)
23. Gepner, D.: New conformal field theories associated with Lie algebras and their partition functions. Nucl. Phys. B285, [FS20] 10-24 (1987)
24. Ginsparg, P.: Curiosities at c = 1. Nucl. Phys. B295, [FS21] 153-170 (1988)
25. Goddard, P.: Meromorphic conformal fields theory. In: Infinite-dimensional Lie algebras and groups. Adv. Ser. Math. Phys. 7 ed. V. Kac, Singapore: World Sci., 1989 pp. 556-587
26. Gorenstein, D.: it Finite Groups. New York: Harper & Row, 1968
27. Harris, G: SU(2) current algebra orbifolds of the Gaussian model. Nucl. Phys. B300, (FS22) 588-610 (1988)
28. Kac, V.: Infinite Dimensional Lie Algebras. Third edition, Cambridge: Cambridge Univ. Press, 1990
29. Kac, V.: Vertex Algebras. In: New Trends in Quantum Field Theory, Proceedings of the 1995 Razlog (Bulgaria)-Workshop, A. Ganchev et al. editors, Sofia: Heron Press, 1996 pp. 261-358
30. Kac, V.G., Peterson, D.H.: Affine Lie algebras and Hecke modular forms. Bull. Amer. Math. Soc. 3, 1057-1061 (1980)
31. Kac, V.G., Peterson, D.H.: Spin and wedge representations of infinite dimensional Lie algebras and groups. Proc. Nat. Acad. Sci. USA 78, 3308-3312 (1981)
32. Kac, V.G., Peterson, D.H.: Infinite dimensional Lie algebras, theta-functions and modular forms. Adv. in Math. 53, 125-264 (1984)
33. Kac, V.G., Radul, A.: Quasi-finite highest weight modules over the Lie algebra of differential operators on the circle. Commun. Math. Phys. 157, 429-457 (1993)
34. 1+∞. Transformation groups 1, 41-70 (1996)
35. Kac, V.G., Wakimoto, M.: Modular and conformal invariance constraints in representation theory of affine algebras. Advances in Math. 70, 156-236 (1988)
36. Kostant, B.: The McKay correspondence, the Coxeter element and representation theory. In: The Mathematical Heritage of Elie Cartan. Soc. Math, de France, Asterisque, hors series, 1985 pp. 209-255
37. Lian, B.H., Zuckerman, G.: Commutative quantum operator algebras. J. Pure Appl. Alg. 100, 117-139 (1995)
38. Longo, R., Rehren, K.-H.: Nets of subfactors. Rev. Math. Phys. 7, 567-597 (1995)
39. 8. Quart. J. Math. Oxford (2) 30, 315-338 (1979)
40. Lusztig, G.: Leading coefficients of character values of Hecke alebras. In: Arcata Conference of Representations of Finite Groups In: Proceedings of Symposium in Pure Math (P. Fong, ed.)47, (1987)
41. 2 current algebras. Teor Mat. Fiz. 92, 507-521 (1992); (American edition: Theor. Math. Phys. 92, 1063 (1993))
42. 2 current algebras. Teor Mat. Fiz. 92, 507-521 (1992); (American edition: Theor. Math. Phys. 92, 1063 (1993))
43. Paunov, R.R., Todorov, I.T.: Modular invariant QFT models of u(1) conformal current algebra. Phys. Lett. B196, 519-526 (1987)
44. Rehren, K.-H.: A new view of the Virasoro algebra. Lett. Math. Phys. 30, 125-130 (1994)
45. Rehren, K.-H., Stanev, Ya.S., Todorov, I.T.: Characterizing invariants for local extensions of current algebras, hep-th/9409165 Commun. Math. Phys. 174, 605-633 (1996)
46. Verlinde, E.: Fusion rules and modular transformations in 2D conformal field theory. Nucl. Phys. B300, [FS22] 360-376 (1988)