Topological sectors and a dichotomy in conformal field theory

Communications in Mathematical Physics

Volumn 251, Issue 2, 2004, Pages 321-364

  Longo, Roberto ^a   Xu, Feng ^b  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 11144248452     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-004-1063-1     Document Type: Article

References (63)

1. Arveson, W.: A Short Course on Spectral Theory. Graduate Texts in Mathematics, 209, New York: Springer-Verlag, 2002
2. Barron, K., Dong, C., Mason, G.: Twisted sectors for tensor product vertex operator algebras associated to permutation groups. Commun. Math. Phys. 227(2), 349-384 (2002)
3. Bertozzini, P., Conti, R., Longo, R.: Covariant sectors with infinite dimension and positivity of the energy. Commun. Math. Phys. 141, 471-492 (1998)
4. Böckenhauer, J., Evans, D.E.: Modular invariants, graphs and α-induction for nets of subfactors I. Commun. Math. Phys. 197, 361-386 (1998)
5. Böckenhauer, J., Evans, D.E.: Modular invariants from subfactors: Type I coupling matrices and intermediate subfactors. Commun. Math. Phys. 213, 267-289 (2000)
6. Böckenhauer, J., Evans, D.E., Kawahigashi, Y.: On α-induction, chiral projectors and modular invariants for subfactors. Commun. Math. Phys. 208, 429-487 (1999)
7. Borisov, L., Halpern, M.B., Schweigert, C.: Systematic approach to cyclic orbifold. Int. J. Mod. Phys. A 13(1), 125-168 (1998)
8. Brunetti, R., Guido, D., Longo, R.: Modular structure and duality in conformal quantum field theory. Commun. Math. Phys. 156, 201-219 (1993)
9. Buchholz, D., Fredenhagen, K.: Locality and structure of particle states. Commun. Math. Phys. 84, 1-54 (1982); Fredenhagen, K.: Localizability of particle states. In: The Algebraic Theory of Superselection Sectors, D. Kastler ed., Singapore, World Scientific, 1990
10. Buchholz, D., Fredenhagen, K.: Locality and structure of particle states. Commun. Math. Phys. 84, 1-54 (1982); Fredenhagen, K.: Localizability of particle states. In: The Algebraic Theory of Superselection Sectors, D. Kastler ed., Singapore, World Scientific, 1990
11. Buchholz, D., Mack, G., Todorov, I.: The current algebra on the circle as a germ of local field theories. Nucl. Phys. B, Proc. Suppl. 5B, 20-56 (1988)
12. Buchholz, D., Schulz-Mirbach, H.: Haag duality in conformal quantum field theory. Rev. Math. Phys. 2, 105-125 (1990)
13. Carey, A.L., Ruijsenaars, S.N.M.: On fermion gauge groups, current algebras and Kac-Moody algebras. Acta Appl. Math. 10, 1-86 (1987)
14. Carpi, S.: The Virasoro algebra and sectors with infinite statistical dimension. Ann. H. Poincaré (to appear), math.OA/0203027
15. Carpi, S.: On the representation theory of Virasoro nets. Commun. Math. Phys. (to appear), math.OA/0306425
16. Connes, A.: Une classification des facteurs de type III. Ann. Sci. Ec. Norm. Sup. 6, 133-252 (1973)
17. Conti, R.: Inclusioni di Algebre di von Neumann e Teoria Algebrica dei Campi. Tesi del Dottorato di Ricerca in Matematica, Università di Roma "Tor Vergata", 1996
18. Dixmier, J.: C*-Algebras Amsterdam: North-Holland, 1982
19. Doplicher, S., Haag, R., Roberts, J.E.: Local observables and particle statistics. I. Commun. Math. Phys. 23, 199-230 (1971); II. 35, 49-85 (1974)
20. Doplicher, S., Haag, R., Roberts, J.E.: Local observables and particle statistics. I. Commun. Math. Phys. 23, 199-230 (1971); II. 35, 49-85 (1974)
21. Doplicher, S., Longo, R.: Standard and split inclusions of von Neumann algebras. Invent. Math. 73, 493-536 (1984)
22. Doplicher, S., Spera, M.: Local normality properties of some infrared representations. Commun. Math. Phys. 89, 19-25 (1983)
23. Evans, D.E., Kawahigashi, Y.: Quantum Symmetries on Operator Algebras. Oxford: Oxford University Press, 1998
24. Fredenhagen, K.: Superselection sectors with infinite statistical dimension. In: "'Subfactors", H. Araki, Y. Kawahigashi, H. Kosaki, eds., Singapore: World Scientific, 1994
25. Gepner, D., Witten, E.: String theory on group manifolds. Nucl. Phys. B278, 493-549 (1986)
26. Guido, D., Longo, R.: Relativistic invariance and charge conjugation in quantum field theory. Commun. Math. Phys. 148, 521-551 (1992)
27. Guido, D., Longo, R.: The conformal spin and statistics theorem. Commun. Math. Phys. 181, 11-35 (1996)
28. Guido, D., Longo, R., Wiesbrock, H.-W.: Extensions of conformal nets and superselection structures. Commun. Math. Phys. 192, 217-244 (1998)
29. Haag, R.: Local Quantum Physics, 2nd ed., Berlin, Heidelberg, New York: Springer-Verlag, 1996
30. Jones, V.F.R.: Index for subfactors. Invent. Math. 72, 1-25 (1983)
31. Kawahigashi, Y., Longo, R.: Classification of local conformal nets. Case c < 1. math-ph/0201015, to appear in Ann. Math.
32. Kawahigashi, Y., Longo, R.: Classification of two-dimensional local conformal nets with c < 1 and 2-cohomology vanishing for tensor categories. Commun. Math. Phys. 244, 63-97 (2004)
33. Kawahigashi, Y., Longo, R., Müger, M.: Multi-interval subfactors and modularity of representations in conformal field theory. Commun. Math. Phys. 219, 631-669 (2001)
34. Kosaki, H.: Type III Factors and Index Theory. Res. Inst. of Math., Lect. Notes 43, Seoul Nat. Univ., 1998
35. Kosaki, H., Longo, R.: A remark on the minimal index of subfactors. J. Funct. Anal. 107, 458-470 (1992)
36. Köster, S.: Local nature of coset models. Preprint 2003, math-ph/0303054
37. Longo, R.: Simple injective subfactors. Adv. in Math. 63, 152-171 (1986)
38. Longo, R.: Index of subfactors and statistics of quantum fields. I. Commun. Math. Phys. 126, 217-247 (1989)
39. Longo, R.: Index of subfactors and statistics of quantum fields. II. Commun. Math. Phys. 130, 285-309 (1990)
40. Longo, R.: Minimal index and braided subfactors. J. Funct. Anal. 109, 98-112 (1992)
41. Longo, R.: A duality for Hopf algebras and for subfactors. I. Commun. Math. Phys. 159, 133-150 (1994)
42. Longo, R.: An analogue of the Kac-Wakimoto formula and black hole conditional entropy. Commun. Math. Phys. 186, 451-479 (1997)
43. Longo, R.: Notes for a quantum index theorem. Commun. Math. Phys. 222, 45-96 (2001)
44. Longo, R.: Conformal subnets and intermediate subfactors. Commun. Math. Phys. 237(1-2), 7-30 (2003)
45. Longo, R.: Work in progress
46. Longo, R., Rehren, K.-H.: Nets of subfactors. Rev. Math. Phys. 7, 567-597 (1995)
47. Longo, R., Roberts, J.E.: A theory of dimension. K-theory 11, 103-159 (1997)
48. Müger, M.: On soliton automorphisms in massive and conformal theories. Rev. Math. Phys. 11(3), 337-359 (1999)
49. Pimsner, M., Popa, S.: Entropy and index for subfactors. Ann. Scient. Ec. Norm. Sup. 19, 57-106 (1986)
50. Rehren, K.-H.: A new view of the Virasoro algebra. Lett. Math. Phys. 30, 125-130 (1994)
51. Rehren, K.-H.: Braid group statistics and their superselection rules. In: "The Algebraic Theory of Superselection Sectors", D. Kastler, ed., Singapore: World Scientific, 1990
52. Roberts, J.E.: Local cohomology and superselection structure. Commun. Math. Phys. 51, 107-119 (1976)
53. Schroer, B., Wiesbrock, H.-W.: Modular theory and geometry. Rev. Math. Phys. 12, 139 (2000) See also: Ebrahimi-Fard, K.: Comments on: Modular theory and geometry, math-ph/0011049
54. Schroer, B., Wiesbrock, H.-W.: Modular theory and geometry. Rev. Math. Phys. 12, 139 (2000) See also: Ebrahimi-Fard, K.: Comments on: Modular theory and geometry, math-ph/0011049
55. ∞ functions defined in a half space. Proc. Am. Math. Soc. 15, 625-626 (1964) Addendum: ibidem 37, 622 (1973)
56. ∞ functions defined in a half space. Proc. Am. Math. Soc. 15, 625-626 (1964) Addendum: ibidem 37, 622 (1973)
57. Takesaki, M.: Theory of Operator Algebras. Vol. I, II, III, Springer Encyclopaedia of Mathematical Sciences 124 (2002), 125, 127 (2003)
58. Xu, F.: New braided endomorphisms from conformal inclusions. Commun. Math. Phys. 192, 347-403 (1998)
59. Xu, F.: Applications of braided endomorphisms from conformal inclusions. Int. Math. Res. Notices 5-23 (1998)
60. Xu, F.: Algebraic orbifold conformal field theory. In: "Mathematical Physics in Mathematics and Physics", R. Longo, ed., Fields Institute Communications Vol. 30, Providence RI: Am. Math. Soc., 2001
61. Xu, F.: Algebraic coset conformal field theories II. Publ. RIMS, Kyoto Univ. 35, 795-824 (1999)
62. Xu, F.: Jones-Wassermann subfactors for disconnected intervals. Commun. Contemp. Math. 2, 307-347 (2000)
63. Xu, F.: Strong additivity and conformal nets. Preprint 2003