Modular invariants from subfactors: Type I coupling matrices and intermediate subfactors

Communications in Mathematical Physics

Volumn 213, Issue 2, 2000, Pages 267-289

  Böckenhauer, Jens ^a   Evans, David E ^a  

^a CARDIFF UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034259847     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200000241     Document Type: Article

References (41)

1. 1. Behrend, R.E., Pearce, P.A., Petkova, V.B., Zuber, J.-B.: Boundary conditions in rational conformal field theories. Nucl. Phys. B570, 525-589 (2000)
2. 2. Böckenhauer, J.: An algebraic formulation of level one Wess-Zumino-Witten models. Rev. Math. Phys. 8, 925-947 (1996)
3. 3. Böckenhauer, J., Evans, D.E.: Modular invariants, graphs and α-induction for nets of subfuctors. I. Commun. Math. Phys. 197, 361-386 (1998)
4. 4. Böckenhuuer, J., Evans, D.E.: Modular invariants, graphs and α-induction for nets of suhfactors. II. Commun. Math. Phys. 200, 57-103 (1999)
5. 5. Böckenhauer, J., Evans, D.E.: Modular invariants, graphs and α-induction for nets of subfactors. III. Commun. Math. Phys. 205, 183-228 (1999)
6. 6. Böckenhauer, J., Evans, D.E., Kawahigashi, Y.: On α-induction, chiral generators and modular invariants for subtactors. Commun. Math. Phys. 208, 429-487 (1999)
7. 7. Böckenhauer, J., Evans, D.E., Kawahigashi, Y.: Chiral structure of modular invariants for subfactors. Commun. Math. Phys. 210, 733-784 (2000)
8. (1)1 conformal invariant theories. Commun. Math. Phys. 113, 1-26 (1987)
9. 9. Di Francesco, P.: Integrable lattice models, graphs and modular invariant conformal field theories. Int. J. Mod. Phys. A7, 407-500 (1992)
10. 10. Di Francesco, P., Zuber, J.-B.: SU (N) lattice integrable models associated with graphs. Nucl. Phys. B338, 602-646 (1990)
11. 11. Di Francesco, P., Zuber, J.-B.: SU (N) lattice integrable models and modular invariance. In: Recent Developments in Conformal Field Theories. Trieste 1989, Singapore: World Scientific, 1990, pp. 179-215
12. 12. Dijkgraaf, R., Verlinde, E.: Modular invariance and the fusion algebras. Nucl. Phys. (Proc. Suppl.) 5B, 87-97 (1988)
13. 13. Doplicher, S., Haag, R., Roberts, J.E.: Fields, observables and gauge transformations. II. Commun. Math. Phys. 15, 173-200 (1969)
14. 14. Evans, D.E., Kawahigashi, Y.: Quantum symmetries on operator algebras. Oxford: Oxford University Press, 1998
15. 15. Fredenhagen, K., Rehren, K.-H., Schroer, B.: Superselection sectors with braid group statistics and exchange algebras. II. Rev. Math. Phys. Special issue, 113-157 (1992)
16. 16. Fröhlich, J., Gabbiani, F.: Braid statistics in local quantum theory. Rev. Math. Phys. 2, 251-353 (1990)
17. 17. Fröhlich, J., Gabbiani, F.: Operator algebras and conformal field theory. Commun. Math. Phys. 155, 569-640 (1993)
18. 18. Fuchs, J., Schellekens, A.N., Schweigert, C.: Galois modular invariants of WZW models. Nucl. Phys. B 437, 667-694 (1995)
19. 19. Gannon, T.: The classification of affine SU (3) modular invariants. Commun. Math. Phys. 161, 233-264 (1994)
20. 20. Guido, D., Longo, R.: The conformal spin and statistics theorem. Commun. Math. Phys. 181, 11-35 (1996)
21. 21. Haag, R.: Local Quantum Physics. Berlin: Springer-Verlag, 1992
22. 22. Izumi, M.: Subalgebras of infinite C*-algebras with finite Watatani indices II: Cuntz-Krieger algebras. Duke Math. J. 91, 409-461 (1998)
23. 23. 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)
24. 24. Jones, V.F.R.: Index for subfactors. Invent. Math. 72, 1-25 (1983)
25. 25. Kac, V.G.: Infinite dimensional Lie algebras, 3rd edition, Cambridge: Cambridge University Press, 1990
26. 26. Kato, A.: Classification of modular invariant partition functions in two dimensions. Mod. Phys. Lett. A2, 585-600 (1987)
27. 27. Longo, R.: Minimal index of braided subfactors. J. Funct. Anal. 109, 98-112 (1991)
28. 28. Longo, R., Rehren, K.-H.: Nets of subfactors. Rev. Math. Phys. 7, 567-597 (1995)
29. 29. Moore, G., Seiberg, N.: Naturality in conformal field theory. Nucl. Phys. B 313, 16-40 (1989)
30. 30. Ocneanu, A.: Paths on Coxeter diagrams: From Platonic solids and singularities to minimal models and subfactors. (Notes recorded by S. Goto.) In: Rajarama Bhat, B. V. et al. (eds.), Lectures on operator theory, The Fields Institute Monographs, Providence, RI: AMS Publications, 2000, pp. 243-323
31. 31. Petkova, V.B., Zuber, J.-B: From CFT to graphs. Nucl. Phys. B 463, 161-193 (1996)
32. 32. Rehren, K.-H.: Braid group statistics and their superselection rules. In: Kastler, D. (ed.): The algebraic theory of superselection sectors. Palermo 1989, Singapore: World Scientific 1990, pp. 333-355
33. 33. Rehren, K.-H.: Space-time fields and exchange fields. Commun. Math. Phys. 132, 461-483 (1990)
34. 34. Rehren, K.-H.: Chiral observables and modular invariants. Commun. Math. Phys. 208, 689-712 (2000)
35. 35. Rehren, K.-H.: Canonical tensor product subfactors. Commun. Math. Phys. 211, 395-406 (2000)
36. 36. Rehren, K.-H., Stanev, Y.S., Todorov, I.T.: Characterizing invariants for local extensions of current algebras. Commun. Math. Phys. 174, 605-633 (1996)
37. 37. Schellekens A.N.,Yankielowicz, S.: Field identification fixed points in the coset construction. Nucl. Phys. B334, 67-102 (1990)
38. 38. Verlinde, E.: Fusion rules and modular transformations in 2D conformal field theory. Nucl. Phys. B 300, 360-376 (1988)
39. 39. Verstegen, D.: New exceptional modular invariant partition functions for simple Kac-Moody algebras. Nucl. Phys. B346, 349-386 (1990)
40. 40. Wassermann, A.: Operator algebras and conformal field theory III: Fusion of positive energy representations of LSU (N) using bounded operators. Invent. Math. 133, 467-538 (1998)
41. 41. Xu, F.: New braided endomorphisms from conformal inclusions. Commun. Math. Phys. 192, 347-403 (1998)