Solitons in affine and permutation orbifolds

Communications in Mathematical Physics

Volumn 253, Issue 3, 2005, Pages 723-764

  Kac, Victor G ^a   Longo, Roberto ^b   Xu, Feng ^c  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF ROME TOR VERGATA   (Italy)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 12444306469     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-004-1160-1     Document Type: Article

References (53)

1. Bantay, P.: Permutation orbifolds. Nucl. Phys. B 633(3), 365-378 (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. Böckenhauer, J., Evans, D.E.: Modular invariants, graphs and α-induction for nets of subfactors I. Commun. Math. Phys. 197, 361-386 (1998)
4. Böckenhauer, J., Evans, D.E., Kawahigashi, Y.: On α-induction, chiral projectors and modular invariants for subfactors. Commun. Math. Phys. 208, 429-487 (1999)
5. Borisov, L., Halpern, M.B., Schweigert, C.: Systematic approach to cyclic orbifold. Internat. J. Modern Phys. A 13(1), 125-168 (1998)
6. Brunetti, R., Guido, D., Longo, R.: Modular structure and duality in conformal quantum field theory. Commun. Math. Phys. 156, 201-219 (1993)
7. 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)
8. 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)
9. Fredenhagen, K., Rehren, K.-H., Schroer, B.: Superselection sectors with braid group statistics and exchange algebras. I. Commun. Math. Phys. 125, 201-226 (1989); II. Rev. Math. Phys. Special issue, 113-157 (1992)
10. Fredenhagen, K., Rehren, K.-H., Schroer, B.: Superselection sectors with braid group statistics and exchange algebras. I. Commun. Math. Phys. 125, 201-226 (1989); II. Rev. Math. Phys. Special issue, 113-157 (1992)
11. Fröhlich, J., Gabbiani, F.: Operator algebras and conformal field theory. Commun. Math. Phys. 155, 569-640 (1993)
12. Guido, D., Longo, R.: Relativistic invariance and charge conjugation in quantum field theory. Commun. Math. Phys. 148, 521-551 (1992)
13. Guido, D., Longo, R.: The conformal spin and statistics theorem. Commun. Math. Phys. 181, 11-35 (1996)
14. Guido, D., Longo, R., Wiesbrock, H.-W.: Extensions of conformal nets and superselection structures. Commun. Math. Phys. 192, 217-244 (1998)
15. Haag, R.: "Local Quantum Physics". 2nd ed., Berlin, Heidelberg, New York: Springer-Verlag, 1996
16. Hiai, F.: Minimizing index of conditional expectations onto subfactors. Publ. Res. Inst. Math. Sci. 24, 673-678 (1988)
17. Izumi, M., Longo, R., Popa, S.: A Galois correspondence for compact groups of automorphisms of von Neumann Algebras with a generalization to Kac algebras. J. Funct. Anal. 155, 25-63 (1998)
18. Jones, V.F.R.: Index for subfactors. Invent. Math. 72, 1-25 (1983)
19. Kac, V.G.: "Infinite Dimensional Lie Algebras". 3rd Edition, Cambridge: Cambridge University Press, 1990
20. 1+∞. Commun. Math. Phys. 190, 57-111 (1997)
21. Kac, V.G., Wakimoto, M.: Modular and conformal invariance constraints in representation theory of affine algebras. Adv. in Math. 70, 156-234 (1988)
22. Karpilovsky, G.: Projective representations of finite groups. Monographs and Textbooks in Pure and Applied Mathematics, Vol.94, New York: Marcel Detter, Inc., 1985
23. Kawahigashi, Y., Longo, R., Müger, M.: Multi-interval subfactors and modularity of representations in conformal field theory. Commun. Math. Phys. 219, 631-669 (2001)
24. Kosaki, H.: "Type III Factors and Index Theory". Res. Inst. Math. Lect. Notes 43, Seoul: Seoul Nat. Univ. Global Analysis Research Center, 1998
25. Kosaki, H., Longo, R.: A remark on the minimal index of subfactors. J. Funct. Anal. 107, 458-470 (1992)
26. Longo, R.: Simple injective subfactors. Adv. Math. 63, 152-171 (1987)
27. Longo, R.: Index of subfactors and statistics of quantum fields. I. Commun. Math. Phys. 126, 217-247 (1989)
28. Longo, R.: Index of subfactors and statistics of quantum fields. II. Commun. Math. Phys. 130, 285-309 (1990)
29. Longo, R.: An analogue of the Kac-Wakimoto formula and black hole conditional entropy. Commun. Math. Phys. 186, 451-479 (1997)
30. Longo, R.: Minimal index and braided subfactors. J. Funct. Anal. 109, 98-112 (1992)
31. Longo, R.: A duality for Hopf algebras and for subfactors. I. Commun. Math. Phys. 159, 133-150 (1994)
32. Longo, R.: Conformal subnets and intermediate subfactors. Commun. Math. Phys. 237(1-2). 7-30 (2003)
33. Longo, R., Rehren, K.-H.: Nets of subfactors. Rev. Math. Phys. 7, 567-597 (1995)
34. Longo, R., Roberts, J.E.: A theory of dimension. K-theory 11, 103-159 (1997)
35. Longo, R., Xu, F.: Topological sectors and a dichotomy in conformal field theory. To appear in Commun. Math. Phys., DOI 10.1007/s00220-004-1063-1, 2004
36. Müger, M.: On soliton automorphisms in massive and conformal theories. Rev. Math. Phys. 11(3), 337-359 (1999)
37. Pimsner, M., Popa, S.: Entropy and index for subfactors. Ann. Scient. Ec. Norm. Sup. 19, 57-106 (1986)
38. Pressley, A., Segal, G.: "Loop Groups". Oxford: Oxford University Press, 1986
39. Rehren, K.-H.: Braid group statistics and their superselection rules. In: "The Algebraic Theory of Superselection Sectors", D. Kastler (ed.), Singapore: World Scientific, 1990
40. Roberts, J.E.: Local cohomology and superselection structure. Commun. Math. Phys. 51, 107-119 (1976)
41. Turaev, V.G.: Quantum invariants of knots and 3-manifolds. Berlin, New York: Walter de Gruyter, 1994
42. Takesaki, M.: "Theory of Operator Algebras". Vol. I, II, III, Springer Encyclopaedia of Mathematical Sciences 124 (2002); 125, 127 (2003)
43. Takesaki, M.: "Theory of Operator Algebras". Vol. I, II, III, Springer Encyclopaedia of Mathematical Sciences 124 (2002); 125, 127 (2003)
44. 2n". Ph.D. dissertation, University of Cambridge, 1997
45. Xu, F.: New braided endomorphisms from conformal inclusions. Commun. Math. Phys. 192, 347-403 (1998)
46. Xu, F.: Applications of braided endomorphisms from conformal inclusions. Int. Math. Res. Notices, 1, 5-23 (1998)
47. Xu, F.: Algebraic orbifold conformal field theories. Proc. Nat. Acad. in Sci. USA, 97(26), 14069-14073 (2000)
48. Xu, F.: Algebraic coset conformal field theories II. Publ. RIMS, Kyoto Univ. 35, 795-824 (1999)
49. Xu, F.: Jones-Wassermann subfactors for disconnected intervals. Commun. Contemp. Math. 2, 307-347 (2000)
50. Xu, F.: On a conjecture of Kac-Wakimoto. Publ. RIMS, Kyoto Univ. 37, 165-190 (2001)
51. Xu, F.: 3-manifold invariants from cosets. math.GT/9907077
52. Xu, F.: Strong additivity and conformal nets. Preprint 2003
53. Xu, F.: Algebraic coset conformal field theories. Commun. Math. Phys. 211, 1-43 (2000)