Modular-invariance of trace functions in Orbifold theory and generalized moonshine

Communications in Mathematical Physics

Volumn 214, Issue 1, 2000, Pages 1-56

  Dong, Chongying ^a   Li, Haisheng ^b   Mason, Geoffrey ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034288951     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200000242     Document Type: Article

References (55)

1. [AM] Anderson, G. and Moore, G.: Rationality in conformal field theory. Commun. Math. Phys. 117, 441-450 (1988)
2. [B1] Borcherds, R.E.: Vertex algebras, Kac-Moody algebras, and the Monster. Proc. Natl. Acad. Sci. USA 83, 3068-3071 (1986)
3. [B2] Borcherds, R.E.: Monstrous moonshine and monstrous Lie superalgebras. Invent. Math. 109, 405-444 (1992)
4. [B3] Borcherds, R.E.: Modular Moonshine III. Peprint
5. [BR] Borcherds, R.E. and Ryba, A.: Modular Moonshine II. Duke. Math. J. 83, 435-459 (1996)
6. [CN] Conway, J.H. and Norton, S.P.: Monstrous Moonshine. Bull. London. Math. Soc. 12, 308-339 (1979)
7. [De] Devoto, J.: Equivariant cohomology and finite groups. Michigan Math. J. 43, 3-32 (1996)
8. [DVVV] Dijkgraaf, R., Vafa, C., Verlinde, E. and Verlinde, H.: The operator algebra of orbifold models. Commun. Math. Phys. 123, 485-526 (1989)
9. [DGH] Dixon, L., Ginsparg, P., Harvey, J.A.: Beauty and the beast: Super-conformal symmetry in a Monster module. Commun. Math. Phys. 119, 221-241 (1986)
10. [DHVW] Dixon, L., Harvey, J.A., Vafa, C. and Witten, E.: Strings on orbifolds. Nucl. Phys. B 261, 620-678 (1985); Strings on orbifolds II. Nucl. Phys. B 274, 285-314 (1986)
11. [DHVW] Dixon, L., Harvey, J.A., Vafa, C. and Witten, E.: Strings on orbifolds. Nucl. Phys. B 261, 620-678 (1985); Strings on orbifolds II. Nucl. Phys. B 274, 285-314 (1986)
12. [DGM] Dolan, L., Goddard, P. and Montague, P.: Conformal field theory of twisted vertex operators. Nucl. Phys. B 338, 529 (1990)
13. [D1] Dong, C.: Vertex algebras associated with even lattices. J. Algebra 160, 245-265. (1993)
14. [D2] Dong, C.: Representations of the moonshine module vertex operator algebra. Contemporary Math. 175 (1994)
15. [D3] Dong, C.: Twisted modules for vertex algebras associated with even lattice. J. of Algebra 165, 91-112 (1994)
16. [DL] Dong, C. and Lepowsky, J.: Generalized Vertex Algebras and Relative Vertex Operators. Progress in Math. Vol. 112, Boston: Birkhäuser, 1993
17. [DLM1] Dong, C., Li, H. and Mason, G.: Some twisted modules for the moonshine vertex operator algebras. Contemp. Math. 193, 25-43 (1996)
18. [DLM2] Dong, C., Li, H. and Mason, G.: Regularity of rational vertex operator algebras. Adv. in Math. 132, 148-166 (1997)
19. [DLM3] Dong, C., Li, H. and Mason, G.: Twisted representations of vertex operator algebras. Math. Ann. 310, 571-600 (1998)
20. [DM1] Dong, C. and Mason, G.: Nonabelian orbifolds and the boson-fermion correspondence. Commun. Math. Phys. 163, 523-559 (1994)
21. [DM2] Dong. C. and Mason, G.: Vertex operator algebras and moonshine: A survey. Adv. Studies in Pure Math. 24, 101-136 (1996)
22. [DM3] Dong, C. and Mason, G.: Monstrous moonshine of higher weight. math.QA/9803116
23. [DMZ] Dong, C., Mason, G. and Zhu, Y.: Discrete series of the Virasoro algebra and the moonshine module. Proc. Symp. Pure. Math. American Math. Soc. 56 II, 295-316 (1994)
24. [EZ] Eichler, M. and Zagier, D.: On the Theory of Jacobi Forms I. Progress in Math. Vol. 55, Boston: Birkhäuser, 1985
25. [FF] Feigin, B.L. and Fuchs, D.B.: Verma modules over the Virasoro algebra. Lecture Notes in Math., Vol. 1060, Berlin-New York: Springer-Verlag, 1984
26. 8. Contemp. Math. 121 (1991)
27. [FHL] Frenkel, I.B., Huang, Y. and Lepowsky, J.: On axiomatic approaches to vertex operator algebras and modules. Memoirs Am. Math. Soc. 104 (1993)
28. [FLM1] Frenkel, I.B., Lepowsky, J. and Meurman, A.: A natural representation of the Fischer-Griess Monster with the modular function J as character. Proc. Natl. Acad. Sci. USA 81, 3256-3260 (1984)
29. [FLM2] Frenkel, I.B., Lepowsky, and Meurman, A.: Vertex operator calculus. In: Mathematical Aspects of String Theory, Proc. 1986 Conference, San Diego, ed. by S.-T. Yau, Singapore: World Scientific, 1987, pp. 150-188
30. [FLM3] Frenkel, I.B., Lepowsky, J. and Meurman, A.: Vertex Operator Algebras and the Monster. Pure and Applied Math. Vol. 134, London-New York: Academic Press, 1988
31. [FZ] Frenkel, I.B. and Zhu, Y: Vertex operator algebras associated to representations of affine and Virasoro algebras. Duke Math. J. 66, 123-168 (1992)
32. [G] Griess, R.: The Friendly Giant. Invent. Math. 69, 1-102 (1982)
33. [HMV] Harvey, J., Moore, G. and Vafa, C.: Quasicrystalline compactification. Nucl. Phys. B304, 269-290 (1988)
34. [H] Huang, Y: A non-meromorphic extension of the moonshine module vertex operator algebra. Contemp. Math. 193, 123-148 (1996)
35. [I] Ince, E.: Ordinary Differential Equations. London: Dover Publications, Inc., 1956
36. [KP] Kac, V. and Peterson, D.: Infinite-dimensional Lie algebras, theta functions and modular forms. Advances in Math. 53, 125-264 (1984)
37. [KM] Knopp, M. and Mason, G.: Generalized modular forms. In preparation
38. [K] Koblitz, N.: Introduction to Ellipitic Curves and Modular Forms. New York: Springer-Verlay, 1984
39. [La] Lang, S.: Introduction to Modular Forms. New York: Springer-Verlag, 1976
40. [Le] Lepowsky, J.: Calculus of twisted vertex operators. Proc. Natl. Acad Sci. USA 82, 8295-8299 (1985)
41. [Li] Li, H.: Local systems of vertex operators, vertex superalgebras and modules. J. Pure Appl. Alg. 109, 143-195 (1996)
42. [M] Montague, P.: Orbifold constructions and the classification of self-dual c = 24 conformal field theory. Nucl. Phys. B 428, 233-258 (1994)
43. [MS] Moore, G. and Seiberg, N.: Classical and quantum conformal field theory. Commun. Math. Phys. 123, 177-254 (1989)
44. [N] Norton, S.: Generalized moonshine. Proc. Symp. Pure. Math., American Math. Soc. 47, 208-209 (1987)
45. [Q] Queen, L.: Some relations between finite groups, Lie groups and modular functions. Ph.D. Thesis, University of Cambridge, 1980
46. [Ra] Rademacher, H.: Topics in Analytic Number Theory. New York: Springer-Verlag, 1973
47. [Ry] Ryba, A.: Modular Moonshine? Contemp. Math. 193, 307-336 (1996)
48. [S] Schellekens, A.N.: Meromorphic c = 24 Conformal Field Theories. Commun. Math. Phys. 153, 159 (1993)
49. [T1] Tuite, M.: Monstrous moonshine from orbifolds. Commun. Math. Phys. 146, 277-309 (1992)
50. [T2] Tuite, M.: On the relationship between monstrous moonshine and the uniqueness of the moonshine module. Commun. Math. Phys. 166, 495-532 (1995)
51. [T3] Tuite, M.: Generalized moonshine and abelian orbifold constructions. Contemp. Math. 193, 353-368 (1996)
52. [V] Vafa, C.: Modular invariance and discrete torsion on orbifolds. Nucl. Phys. B 273, 592 (1986)
53. [Wa] Wang, W.: Rationality of Virasoro vertex operator algebras. Duke Math. J. IMRN, 711, 197-211 (1993)
54. [Wo] Wohlfahrt, K.: An extension of F. Klein's level concept. Illinois J. Math. 8, 529-535 (1964)
55. [Z] Zhu, Y.: Modular invariance of characters of vertex operator algebras. J. Am. Math. Soc. 9, 237-302 (1996)