Open-string vertex algebras, tensor categories and operads

Communications in Mathematical Physics

Volumn 250, Issue 3, 2004, Pages 433-471

  Huang, Yi Zhi ^a   Kong, Liang ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 7444225253     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-004-1059-x     Document Type: Article

References (44)

1. [BPZ] Belavin, A.A., Polyakov, A.M., Zamolodchikov, A.B.: Infinite conformal symmetries in two-dimensional quantum field theory. Nucl. Phys. B241, 333-380 (1984)
2. [B] Borcherds, R.E.: Vertex algebras, Kac-Moody algebras, and the Monster. Proc. Natl. Acad. Sci. USA 83, 3068-3071 (1986)
3. [DMS] Di Francesco, P., Mathieu, P., Sénéchal, D.: Conformal field theory. Graduate Texts in Contemporary Physics. New York: Springer-Verlag, 1997
4. [DF] Dotsenko, V.S., Fateev, V.A.: Conformal algebra and multipoint correlation functions in 2d statistical models. Nucl. Phys. B240, 312-348 (1984)
5. [C1] Cardy, J.L.: Conformal invariance and surface critical behavior. Nucl. Phys. B240, 514-532 (1984)
6. [C2] Cardy, J.L.: Effect of boundary conditions on the operator content of two-dimensional conformally invariant theories. Nucl. Phys. B275, 200-218 (1986)
7. [C3] Cardy, J.L.: Boundary conditions, fusion rules and the Verlinde formula. Nucl. Phys. B324, 581-596 (1989)
8. [D] Douglas, M.R.: Dirichlet branes, homological mirror symmetry, and stability. In: Proceedings of the International Congress of Mathematicians, Vol. III (Beijing, 2002), Beijing: Higher Ed. Press, 2002, pp. 395-408
9. [FRW] Feingold, A.J., Ries, J.F.X., Weiner, M.D.: Spinor construction of the c = 1/2 minimal model. In: Moonshine, the Monster, and related topics. Proc. Joint Summer Research Conference, Mount Holyoke College, South Hadley, 1994, (eds.), C. Dong, G. Mason, Contemp. Math. 193, Providence, RI: Am. Math. Soc., 1996, pp. 45-92
10. [FFFS] Felder, G., Fröhlich, J., Fuchs, J., Schweigert, C.: Correlation functions and boundary conditions in rational conformal field theory and three-dimensional topology. Compositio Math. 131, 189-237 (2002)
11. [FHL] Frenkel, I.B., Huang, Y.-Z., Lepowsky, J.: On axiomatic approaches to vertex operator algebras and modules. Preprint, 1989; Mem. Amer. Math. Soc. 104, (1993)
12. [FLM] Frenkel, I.B., Lepowsky, J., Meurman, A.: Vertex operator algebras and the Monster. Pure and Appl. Math. 134, New York: Academic Press, 1988
13. [FRS1] Fuchs, J., Runkel, I., Schweigert, C.: Conformal correlation functions, Frobenius algebras and triangulations. Nucl. Phys. B624, 452-468 (2002)
14. [FRS2] Fuchs, J., Runkel, I., Schweigert, C.: TFT construction of RCFT correlators I: Partition functions. To appear; hep-th/0204148
15. [HK1] Hu, P., Kriz, I.: Conformal field theory and elliptic cohomology. To appear
16. [HK2] Hu, P., Kriz, I.: D-brane cohomology and elliptic cohomology. To appear
17. [H1] Huang, Y.-Z.: On the geometric interpretation of vertex operator algebras. Ph.D thesis, Rutgers University, 1990
18. [H2] Huang, Y.-Z.: Geometric interpretation of vertex operator algebras. Proc. Natl. Acad. Sci. USA 88, 9964-9968 (1991)
19. [H3] Huang, Y.-Z.: A theory of tensor products for module categories for a vertex operator algebra, IV. J. Pure Appl. Alg. 100, 173-216 (1995)
20. [H4] Huang, Y.-Z.: Virasoro vertex operator algebras, (nonmeromorphic) operator product expansion and the tensor product theory. J. Alg. 182, 201-234 (1996)
21. [H5] Huang, Y.-Z.: A nonmeromorphic extension of the moonshine module vertex operator algebra. In: Moonshine, the Monster and related topics, Proc. Joint Summer Research Conference, Mount Holyoke, 1994, (eds.), C. Dong, G. Mason, Contemp. Math., Vol. 193, Providence, RI: Am. Math. Soc., 1996, pp. 123-148
22. [H6] Huang, Y.-Z.: Two-dimensional conformal geometry and vertex operator algebras. Progress in Mathematics, Vol. 148, Boston: Birkhäuser, 1997
23. [H7] Huang, Y.-Z.: Generalized rationality and a "Jacobi identity" for intertwining operator algebras. Selecta Math. (N. S.) 6, 225-267 (2000)
24. [H8] Huang, Y.-Z.: Differential equations and intertwining operators. Duke Math. J., to appear; math.QA/0206206
25. [H9] Huang, Y.-Z.: Riemann surfaces with boundaries and the theory of vertex operator algebras. To appear; math.QA/0212308
26. [HKL] Huang, Y.-Z., Kirillov, A., Jr., Lepowsky, J.: Braided tensor categories and extensions of vertex operator algebras. To appear
27. [HL1] Huang, Y.-Z., Lepowsky, J.: 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 College, South Hadley, 1992, (eds.), P. Sally, M. Flato, J. Lepowsky, N. Reshetikhin, G. Zuckerman, Contemp. Math., Vol. 175, Providence, RI: Am. Math. Soc., 1994, pp. 131-148
28. [HL2] Huang, Y.-Z., Lepowsky, J.: Vertex operator algebras and operads. In: The Gelfand Mathematical Seminars, 1990-1992, (eds.), L. Corwin, I. Gelfand, J. Lepowsky, Boston: Birkhäuser, 1993, pp. 145-161
29. [HL3] Huang, Y.-Z., Lepowsky, J.: A theory of tensor products for module categories for a vertex operator algebra, I. Selecta Math. (N.S.) 1, 699-756 (1995)
30. [HL4] Huang, Y.-Z., Lepowsky, J.: A theory of tensor products for module categories for a vertex operator algebra, II. Selecta Math. (N.S.) 1, 757-786 (1995)
31. [HL5] Huang, Y.-Z., Lepowsky, J.: Tensor products of modules for a vertex operator algebra and vertex tensor categories. In: Lie Theory and Geometry, in honor of Bertram Kostant, (eds.), R. Brylinski, J.-L. Brylinski, V. Guillemin, V. Kac, Boston: Birkhäuser, 1994, pp. 349-383
32. [HL6] Huang, Y.-Z., Lepowsky, J.: A theory of tensor products for module categories for a vertex operator algebra, III. J. Pure Appl. Alg. 100, 141-171 (1995)
33. [K] Kong, L.: Ph. D. Thesis, Rutgers University, in preparation
34. [L] Lazaroiu, C.I.: On the structure of open-closed topological field theory in two dimensions. Nucl. Phys. B603, 497-530 (2001)
35. [M1] Moore, G.: Some comments on branes, G-flux, and K-theory. Int. J. Mod. Phys. A16, 936-944 (2001)
36. [M2] Moore, G.: D-branes, RR-Fields and K-Theory, I, II, III, VI. In: Lecture notes for the ITP miniprogram: The duality workshop: a Math/Physics collaboration, June, 2001; http://online.itp.ucsb.edu/online/mp01/moore1
37. [M3] Moore, G.: K-Theory from a physical perspective. To appear; hep-th/0304018
38. [O] Ostrik, V.: Module categories, weak Hopf algebras and modular invariants. Transform. Groups 8, 177-206 (2003)
39. [S1] Segal, G.: The definition of conformal field theory. In: Differential geometrical methods in theoretical physics (Como, 1988), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 250, Dordrecht: Kluwer Acad. Publ., 1988, pp. 165-171
40. [S2] Segal, G.B.: The definition of conformal field theory. Preprint, 1988
41. [S3] Segal, G.B.: Two-dimensional conformal field theories and modular functors. In: Proceedings of the IXth International Congress on Mathematical Physics, Swansea, 1988, Bristol: Hilger, 1989, pp. 22-37
42. [S4] Segal, G.: Topological structures in string theory. R. Soc. Lond. Philos. Trans. A359, 1389-1398 (2001)
43. [V] Voronov, A.A.: The Swiss-cheese operad. In: Homotopy invariant algebraic structures, in honor of J. Michael Boardman, Proc. of the AMS Special Session on Homotopy Theory, Baltimore, 1998, (eds.), J.-P. Meyer, J. Morava, W. S. Wilson, Contemp. Math., Vol. 239, Providence, RI: Am. Math. Soc., 1999, pp. 365-373
44. [W] Wang, W.: Rationality of Virasoro vertex operator algebras. Int. Math. Res. Notices (in Duke Math. J.) 7, 197-211 (1993)