|
Intertwining operator superalgebras and vertex tensor categories for superconformal algebras, II
Author(s):
Yi-Zhi
Huang;
Antun
Milas
Journal:
Trans. Amer. Math. Soc.
354
(2002),
363-385.
MSC (1991):
Primary 17B69, 17B68;
Secondary 17B65, 81R10, 81T40, 81T60
Posted:
August 21, 2001
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We construct the intertwining operator superalgebras and vertex tensor categories for the superconformal unitary minimal models and other related models.
References:
-
- [A1]
- D. Adamovic, Representations of the
vertex operator superalgebra, Internat. Math. Res. Notices 1999 (1999), 62-79. MR 99m:17032 - [A2]
- D. Adamovic, Rationality of unitary
vertex operator superalgebras, math.QA/9909055, to appear. - [A3]
- D. Adamovic, Vertex algebra approach to fusion rules for
superconformal minimal models, to appear. - [AM]
- D. Adamovic and A. Milas, Vertex operator algebras associated to modular invariant representations for
, Math. Res. Lett. 2 (1995), 563-575. MR 96m:17047 - [Ba1]
- K. Barron, The supergeometric interpretation of vertex operator superalgebras, Ph.D. thesis, Rutgers University, 1996.
- [Ba2]
- K. Barron,
Neveu-Schwarz vertex operator superalgebras over Grassmann algebras and with odd formal variables, in: Representations and quantizations (Shanghai, 1998), China High. Educ. Press, Beijing, 2000, pp. 9-35. CMP 2001:06 - [D]
- M. Doerrzapf, The embedding structure of unitary
minimal models, Nucl. Phys. B529 (1998), 639-655. - [DMZ]
- C. Dong, G. Mason and Y. Zhu, Discrete series of the Virasoro algebra and the moonshine module, in: Algebraic groups and their generalizations: quantum and infinite-dimensional methods (University Park, PA, 1991), Proc. Sympos. Pure Math., Vol. 56, Part 2, Amer. Math. Soc., Providence, RI, 1994, 295-316. MR 95c:17043
- [EG]
- W. Eholzer and M. R. Gaberdiel, Unitarity of rational
superconformal theories, Comm. Math. Phys. 186 (1997), 61-85. MR 99e:81075 - [FF]
- B. Feigin and E. Frenkel, Integrals of motion and quantum groups, in: Integrable systems and quantum groups (Montecatini Terme, 1993), Lecture Notes in Math., Vol. 1620, Springer, Berlin, 1996, 349-418. MR 97d:58093
- [FHL]
- I. B. Frenkel, Y.-Z. Huang and J. Lepowsky, On axiomatic approaches to vertex operator algebras and modules, preprint, 1989; Memoirs Amer. Math. Soc. 104, 1993. MR 94a:17007
- [FLM]
- I. B. Frenkel, J. Lepowsky, and A. Meurman, Vertex operator algebras and the Monster, Pure and Appl. Math., 134, Academic Press, New York, 1988. MR 90h:17026
- [FS]
- B. L. Feigin and A. M. Semikhatov, Free-field resolutions of the unitary
super-Virasoro representations, hep-th/9810059, to appear. - [FSST]
- B. L. Feigin, A. M. Semikhatov, V. A. Sirota and I. Y. Tipunin, Resolutions and characters of irreducible representations of the
superconformal algebra, Nucl. Phys. B536 (1999), 617-656. MR 2000a:81077 - [FST]
- B. L. Feigin, A. M. Semikhatov and I. Y. Tipunin, Equivalence between chain categories of representations of affine
and superconformal algebras, J. Math. Phys. 39 (1998), 3865-3905. MR 2000i:81047 - [FZ]
- I. B. Frenkel and Y. Zhu, Vertex operator algebras associated to representations of affine and Virasoro algebras, Duke Math. J. 66 (1992), 123-168. MR 93g:17045
- [Ge1]
- D. Gepner, Exactly solvable string compactifications on manifolds of
holonomy, Phys. Lett. B199 (1987), 380-388. MR 89h:83035 - [Ge2]
- D. Gepner, Space-time supersymmetry in compactified string theory and superconformal models, Nucl. Phys. B296 (1988), 757-778. MR 89b:81189
- [Gr]
- B. R. Greene, Aspects of quantum geometry, in: Mirror Symmetry III, Proceedings of the Conference on Complex Geometry and Mirror Symmetry, Montréal, 1995, Stud. Adv. Math., Vol. 10, Amer. Math. Soc., Internat. Press and Centre de Recherches Math., 1-67. MR 2000e:81256
- [GP]
- B. R. Greene and M. R. Plesser, Duality in Calabi-Yau moduli space, Nucl. Phys. B338 (1990), 15-37. MR 91h:32018
- [H1]
- Y.-Z. Huang, A theory of tensor products for module categories for a vertex operator algebra, IV, J. Pure Appl. Alg., 100 (1995), 173-216. MR 98a:17050
- [H2]
- Y.-Z. Huang, Virasoro vertex operator algebras, (nonmeromorphic) operator product expansion and the tensor product theory, J. Alg. 182 (1996), 201-234. MR 97h:17029
- [H3]
- Y.-Z. Huang, Intertwining operator algebras, genus-zero modular functors and genus-zero conformal field theories, in: Operads: Proceedings of Renaissance Conferences, ed. J.-L. Loday, J. Stasheff, and A. A. Voronov, Contemporary Math., 202, Amer. Math. Soc., Providence, 1997, 335-355. MR 98a:17051
- [H4]
- Y.-Z. Huang, Two-dimensional conformal geometry and vertex operator algebras, Progress in Mathematics, Vol. 148, Birkhäuser, Boston, 1997. MR 98i:17037
- [H5]
- Y.-Z. Huang, Genus-zero modular functors and intertwining operator algebras, Internat. J. Math. 9 (1998), 845-863. MR 99i:17031
- [H6]
- Y.-Z. Huang, Generalized rationality and a generalized Jacobi identity for intertwining operator algebras, Selecta Math. (N.S.) 6 (2000), 225-267.
- [HL1]
- Y.-Z. Huang and J. Lepowsky,
Toward a theory of tensor products for representations of a vertex operator algebra, in: Proc. 20th International Conference on Differential Geometric Methods in Theoretical Physics, New York, 1991, ed. S. Catto and A. Rocha, World Scientific, Singapore, 1992, Vol. 1, 344-354. MR 94k:17045 - [HL2]
- Y.-Z. Huang and J. Lepowsky, Operadic formulation of the notion of vertex operator algebra, in: Mathematical Aspects of Conformal and Topological Field Theories and Quantum Groups, Proc. Joint Summer Research Conference, Mount Holyoke, 1992, ed. P. Sally, M. Flato, J. Lepowsky, N. Reshetikhin and G. Zuckerman,
Contemporary Math., Vol. 175, Amer. Math. Soc., Providence, 1994, 131-148. MR 95m:17022 - [HL3]
- Y.-Z. Huang and J. Lepowsky, Tensor products of modules for a vertex operator algebra and vertex tensor categories, in: Lie Theory and Geometry, in honor of Bertram Kostant, ed. R. Brylinski, J.-L. Brylinski, V. Guillemin, and V. Kac, Birkhäuser, Boston, 1994, 349-383. MR 96e:17061
- [HL4]
- Y.-Z. Huang and J. Lepowsky, A theory of tensor products for module categories for a vertex operator algebra, I, Selecta Mathematica, New Series 1 (1995), 699-756. MR 98a:17047
- [HL5]
- Y.-Z. Huang and J. Lepowsky, A theory of tensor products for module categories for a vertex operator algebra, II, Selecta Mathematica, New Series 1 (1995), 757-786. MR 98a:17047
- [HL6]
- Y.-Z. Huang and J. Lepowsky, A theory of tensor products for module categories for a vertex operator algebra, III, J. Pure Appl. Alg. 100 (1995), 141-171. MR 98a:17049
- [HL7]
- Y.-Z. Huang and J. Lepowsky, Intertwining operator algebras and vertex tensor categories for affine Lie algebras, Duke Math. J. 99 (1999), 113-134. CMP 99:16
- [HL8]
- Y.-Z. Huang and J. Lepowsky, A theory of tensor products for module categories for a vertex operator algebra, V, to appear.
- [HM]
- Y.-Z. Huang and A. Milas, Intertwining operator superalgebras and vertex tensor categories for superconformal algebras, I, math.QA/9909039, IHES preprint IHES/M/99/69, to appear;
- [HZ]
- Y.-Z. Huang and W. Zhao, Semi-infinite forms and topological vertex operator algebras, Commun. Contemp. Math. 2 (2000), 191-241. CMP 2000:13
- [L]
- B. Lian, On the classification of simple vertex operator algebras, Comm. Math. Phys. 163 (1994), 307-357. MR 95i:17033
Similar Articles:
Retrieve articles in Transactions of the American Mathematical Society
with MSC
(1991):
17B69, 17B68,
17B65, 81R10, 81T40, 81T60
Retrieve articles in all Journals with MSC
(1991):
17B69, 17B68,
17B65, 81R10, 81T40, 81T60
Additional Information:
Yi-Zhi
Huang
Affiliation:
Department of Mathematics, Kerchof Hall, University of Virginia, Charlottesville, Virginia 22904-4137 {\it and} Department of Mathematics, Rutgers University, 110 Frelinghuysen Rd., Piscataway, New Jersey 08854-8019 (permanent address)
Email:
yzhuang@math.rutgers.edu
Antun
Milas
Affiliation:
Department of Mathematics, Rutgers University, 110 Frelinghuysen Rd., Piscataway, New Jersey 08854-8019
Email:
amilas@math.rutgers.edu
DOI:
10.1090/S0002-9947-01-02869-0
PII:
S 0002-9947(01)02869-0
Keywords:
$N=2$ superconformal algebras,
intertwining operator superalgebras,
vertex tensor categories
Received by editor(s):
April 18, 2000
Received by editor(s) in revised form:
February 21, 2001
Posted:
August 21, 2001
Additional Notes:
The research of Y.-Z. H. is supported in part by NSF grants DMS-9622961 and DMS-0070800.
The research of A. M. is supported in part by NSF grants.
Copyright of article:
Copyright
2001,
American Mathematical Society
|