Rationality, quasirationality and finite W-algebras

Communications in Mathematical Physics

Volumn 238, Issue 1-2, 2003, Pages 305-331

  Gaberdiel, Matthias R ^a,b   Neitzke, Andrew ^a,c  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b KING'S COLLEGE LONDON   (United Kingdom)

^c HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037660883     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-003-0845-1     Document Type: Article

References (35)

1. Belavin, A.A., Polyakov, A.M., Zamolodchikov, A.B.: Infinite conformal symmetry in two-dimensional quantum field theory. Nucl. Phys. B241, 333-380 (1984)
2. Borcherds, R.E.: Vertex algebras, Kac-Moody algebras, and the Monster. Proc. Natl. Acad. Sci. USA 83, 3068-3071 (1986)
3. Borcherds, R.E.: Monstrous moonshine and monstrous Lie superalgebras. Invent. Math. 109, 405-444 (1992)
4. Brungs, D., Nahm, W.: The associative algebras of conformal field theory. Lett. Math. Phys. 47, 379-383 (1999), hep-th/9811239
5. Di Francesco, P., Mathieu, P., Sénechal, D.: Conformal field theory. Berlin-Heidelberg-New York: Springer, 1997
6. Dong, C., Li, H., Mason, G.: Twisted representations of vertex operator algebras. Math. Ann. 310(3), 571-600 (1998), q-alg/9509005
7. Dong, C., Li, H., Mason, G.: Modular invariance of trace functions in orbifold theory. q-alg/9703016
8. Eholzer, W., Flohr, M., Honecker, A., Hübel, R., Nahm, W., Varnhagen, R.: Representations of W-algebras with two generators and new rational models. Nucl. Phys. B383, 249-290 (1992)
9. Farb, B., Dennis, R.K.: Noncommutative Algebra. Berlin-Heidelberg-New York: Springer, 1993
10. Frenkel, I., Huang, Y.-Z., Lepowsky, J.: On axiomatic approaches to vertex operator algebras and modules. Mem. Am. Math. Soc. 104, 1-64 (1993)
11. Frenkel, I., Zhu, Y.: Vertex operator algebras associated to representations of affine and Virasoro algebras. Duke Math. J. 66, 123-168 (1992)
12. Frenkel, I., Lepowsky, J., Meurman, A.: Vertex operator algebras and the Monster. Pure and Applied Mathematics 134, New York: Academic, 1988
13. Friedan, D., Shenker, S.: The analytic geometry of two-dimensional conformal field theory. Nucl. Phys. B281, 509-545 (1987)
14. Gannon, T.: Monstrous moonshine and the classification of CFT. math. QA/9906167
15. Gaberdiel, M.R.: An introduction to conformal field theory. Rept. Prog. Phys. 63, 607-667 (2000), hep-th/9910156
16. Gaberdiel, M.R., Goddard, P.: Axiomatic conformal field theory. Commun. Math. Phys. 209, 549-594 (2000), hep-th/9810018
17. Gaberdiel, M.R., Kausch, H.G.: A rational logarithmic conformal field theory. Phys. Lett. B386, 131-137 (1996), hep-th/9606050
18. Griffiths, P., Harris, J.: Principles of algebraic geometry. New York: Wiley, 1978
19. Huang, Y.-Z.: Geometric interpretation of vertex operator algebras. Proc. Nat. Acad. Sci. USA 88, 9964-9968 (1991)
20. Huang, Y.-Z.: Two-dimensional conformal geometry and vertex operator algebras. Progress in Mathematics 148, Boston: Birkhäuser, 1997
21. Huang, Y.-Z.: A functional-analytic theory of vertex (operator) algebras. Commun. Math. Phys. 204, 61-84 (1999)
22. Kac, V.: Vertex algebras for beginners. Providence, RI: American Mathematical Society, 1997
23. Karel, M., Li, H.: Certain generating subspaces for vertex operator algebras. J. Alg. 217, 393-421 (1999), math. QA/9807111
24. Li, H.: Some finiteness properties of regular vertex operator algebras. J. Alg. 212, 495-514 (1999), math. QA/9807077
25. Li, H.: Representation theory and tensor product theory for vertex operator algebras Ph.D. thesis, Rutgers University, 1994, hep-th/9406211
26. Li, H.: Determining fusion rules by A(V)-modules and bimodules. J. Alg. 212, 515-556 (1999)
27. Li, H.: The regular representation, Zhu's A(V)-theory and induced modules, math.QA/9909007
28. Moore, G., Seiberg, N.: Polynomial equations for rational conformal field theories. Phys. Lett. B212, 451-460 (1988)
29. Moore, G., Seiberg, N.: Classical and quantum conformal field theory. Commun. Math. Phys. 123, 177-254 (1989)
30. Nahm, W.: Quasi-rational fusion products. Int. J. Mod. Phys. B8, 3693-3702 (1994), hep-th/9402039
31. Neitzke, A.: Zhu's algebra and an algebraic characterization of chiral blocks, hep-th/0005144
32. Polchinski, J., Cai, Y.: Consistency of open superstring theories. Nucl. Phys. B296, 91-150 (1988)
33. Segal, G.B.: Notes on conformal field theory. Unpublished manuscript
34. Watts, G.M.T.: W algebras and coset models. Phys. Lett. B245, 65-71 (1990)
35. Zhu, Y.: Modular invariance of characters of vertex operator algebras. J. Amer. Math. Soc. 9, 237-302 (1996)