Limits and degenerations of unitary conformal field theories

Communications in Mathematical Physics

Volumn 251, Issue 3, 2004, Pages 589-643

  Roggenkamp, Daniel ^a,b   Wendland, Katrin ^c  

^a UNIVERSITY OF BONN   (Germany)

^b KING'S COLLEGE LONDON   (United Kingdom)

^c UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 10044297499     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-004-1131-6     Document Type: Article

References (62)

1. [A-G-S-G] Alvarez-Gaumé, L., Sierra, G., Gomez, C.: Topics in conformal field theory. In: Physics and mathematics of strings, Teaneck, NJ: World Sci. Publishing, 1990, pp. 16-184
2. [A-G-M] Aspinwall, P.S., Greene, B.R., Morrison, D.R.: Calabi-Yau moduli space, mirror manifolds and spacetime topology change in string theory. Nucl. Phys. B416, 414-480 (1994)
3. [A-M] Aspinwall, P.S., Morrison, D.R.: String theory on K3 surfaces. In: Greene, B., Yau, S.T. (eds): Mirror symmetry, vol. II, 1994, pp. 703-716
4. [B-P-Z] Belavin, A.A., Polyakov, A.M., Zamolodchikov, A.B.: Infinite conformal symmetry in two-dimensional quantum field theory. Nucl. Phys. B241, 333-380 (1984)
5. [B-G-V] Berline, N., Getzler, E., Vergne, M.: Heat kernels and Dirac operators. Berlin-Heidelberg-New York: Springer-Verlag, 1992
6. [Bo] Bourbaki, N.: Éléments de mathématique. Théorie des ensembles. Paris: Hermann, 1970
7. [B-N] Brungs, D., Nahm, W.: The associative algebras of conformal field theory. Lett. Math. Phys. 47(4), 379-383 (1999)
8. (1) conformal invariant theories. Commun. Math. Phys. 113, 1-26 (1987)
9. [C-I-Z2] Cappelli, A., Itzykson, C., Zuber, J.B.: Modular invariant partition functions in two dimensions. Nucl. Phys. B280, 445-465 (1987)
10. [C-E-N-T] Casher, A., Englert, F., Nicolai, H., Taormina, A.: Consistent superstrings as solutions of the D = 26 bosonic string theory. Phys. Lett. B162, 121-126 (1985)
11. [C-G1] Cheeger, J., Gromov, M.: Collapsing Riemannian manifolds while keeping their curvature bounded. I. J. Diff. Geom. 23(3), 309-346 (1986)
12. [C-G2] Cheeger, J., Gromov, M.: Collapsing Riemannian manifolds while keeping their curvature bounded. II. J. Diff. Geom. 32(1), 269-298 (1990)
13. [Co1] Connes, A.: Noncommutative differential geometry. Inst. Hautes Études Sci. Publ. Math., 62, 257-360 (1985)
14. [Co2] Connes, A.: Géométrie non commutative. Paris: InterEditions, 1990
15. [Co3] Connes, A.: Gravity coupled with matter and the foundation of non-commutative geometry. Commun. Math. Phys. 182(1), 155-176 (1996)
16. [D-V-V] Dijkgraaf, R., Verlinde, E., Verlinde, H.: c = 1 Conformal field theories on Riemann surfaces. Commun. Math. Phys. 115, 646-690 (1988)
17. [D-V-V-V] Dijkgraaf, R., Vafa, C., Verlinde, E., Verlinde, H.: The operator algebra of orbifold models. Commun. Math. Phys. 123, 485-543 (1989)
18. [D-F-M-S] Dixon, L.J., Friedan, D., Martinec, E., Shenker, S.: The conformal field theory of orbifolds. Nucl. Phys. B282, 13-73 (1987)
19. [Do] Dold, A.: Lectures on algebraic topology. Die Grundlehren der mathematischen Wissenschaften, Vol. 200, Berlin-Heidelberg-New York: Springer-Verlag, 1972
20. [D-F1] Dotsenko, V.S., Fateev, V.A.: Conformal algebra and multipoint correlation functions in 2D statistical models. Nucl. Phys. B240, 312-348 (1984)
21. [D-F2] Dotsenko, V.S., Fateev, V.A.: Four-point correlation functions and the operator algebra in 2D conformal invariant theories with central charge C ≤ 1. Nucl. Phys. B251, 691-769 (1985)
22. [D-F3] Dotsenko, V.S., Fateev, V.A.: Operator algebra of two-dimensional conformal field theories with central charge c ≤ 1. Phys. Lett. B154, 291-295 (1985)
23. [D-H-V-W] Dixon, L.J., Harvey, J., Vafa, C., Witten, E.: Strings on orbifolds II. Nucl. Phys. B274, 285-314 (1986)
24. [F-F] Feigin, B.L., Fuks, D.B.: Moscow preprint. 1983
25. [Fe1] Felder, G.: BRST approach to minimal models. Nucl. Phys. B317, 215-236 (1989)
26. [Fe2] Felder, G.: Erratum: BRST approach to minimal models. Nucl. Phys. B324, 548 (1989)
27. [F-R] Forste, S., Roggenkamp, D.: Current-current deformations of conformal field theories, and WZW models. IHEP 0305, 71 (2003)
28. [F-M-S] Di Francesco, P., Mathieu, P., Sénéchal, D.: Conformal field theory. Graduate Texts in Contemporary Physics, New York-Berlin-Heidelberg: Springer-Verlag, 1996
29. [Fr-S] Fredenhagen, S., Schomerus, V.: D-branes in coset models. JHEP 02, 005 (2002)
30. [F-G] Fröhlich, J., Gawȩdzki, K.: Conformal field theory and geometry of strings. In: Mathematical quantum theory. I. Field theory and many-body theory (Vancouver, BC, 1993). Providence, RI: Am. Math. Soc., 1994, pp. 57-97
31. [F-G-R] Fröhlich, I., Grandjean, O., Recknagel, A.: Supersymmetric quantum theory, non-commutative geometry, and gravitation. In: Symétries quantiques (Les Houches, 1995). Amsterdam: North-Holland, 1998, pp. 221-385
32. [Fu-S] Fuchs, J., Schweigert, C.: WZW fusion rings in the limit of infinite level. Commun. Math. Phys. 185, 641-670 (1997)
33. [Gab] Gaberdiel, M.R.: D-branes from conformal field theory. In: Proceedings of the Workshop on the Quantum Structure of Spacetime and the Geometric Nature of Fundamental Interactions, Corfu, Greece, 13-20 September 2001; http://arxiv.org/abs/hep-th/0201113, 2002
34. [G-G] Gaberdiel, M.R., Goddard, P.: Axiomatic conformal field theory. Commun. Math. Phys. 209, 549-594 (2000)
35. [G-N] Gaberdiel, M.R., Neitzke, A.: Rationality, quasirationality and finite W-algebras. Commun. Math. Phys. 238, 305-331 (2003)
36. [Gaw] Gawȩdzki, K.: Boundary WZW, G/H, G/G and CS theories. Annales Henri Poincaré In: Fields Strings and Critical Phenomena, E. Brézin, J. Zinn-Justin(eds.), 3, 847-881 (2002)
37. [Gi] Ginsparg, P.: Applied conformal field theory. Lectures given at the Les Houches Summer School in Theoretical Physics 1988 (Les Houches, France), London: Elsevier, 1989, pp. 1-168
38. [G-R-W] Graham, K., Runkel, I., Watts, G.M.T.: Minimal model boundary flows and c = 1 CFT. Nucl. Phys. B608, 527-556 (2001)
39. [Gr] Gross, M.: Topological mirror symmetry. Invent. Math. 144(1), 75-137 (2001)
40. [He] Henrici, P.: Essentials of numerical analysis with pocket calculator demonstrations. New York: John Wiley & Sons Inc., 1982
41. [I-S-Z] Itzykson, C., Saleur, H., Zuber, J.-B. (eds): Conformal invariance and applications to statistical mechanics. Singapore: World Scientific, 1988
42. [Ka] Kadanoff, L.P.: Multicritical behaviour at the Kosterlitz-Thouless Critical Point. Ann. Physics 120, 39-71 (1979)
43. [K-S] Kontsevich, M., Soibelman, Y.: Homological mirror symmetry and torus fibrations. In: Symplectic geometry and mirror symmetry (Seoul, 2000). River Edge, NJ: World Sci. Publishing, 2001, pp. 203-263
44. [Lo] Lord, S.: Riemannian Geometries. http://arxiv.org/abs/math-ph/ 0010037, 2000
45. [M-M-S] Maldacena, J., Moore, G., Seiberg, N.: Geometrical interpretation of D-branes in gauged WZW models. JHEP 07, 046 (2001)
46. [M-S1] Moore, G., Seiberg, N.: Classical and quantum conformal field theory. Commun. Math. Phys. 123, 177-253 (1989)
47. [M-S2] Moore, G., Seiberg, N.: Naturality in conformal field theory. Nucl. Phys. B313, 16 (1989)
48. [Mo] Morrison, D.R.: Where is the large radius limit? In: Halpern, M.B., et. al (eds): Proceedings of Strings '93, Berkeley, CA, USA, May 24-29, 1993. Singapore: World Scientific, pp. 311-315
49. [Nah] Nahm, W.: On quasi-rational conformal field theories. Nucl. Phys. B (Proc. Suppl.) 49, 107-114 (1996)
50. [Nar] Narain, K.S.: New heterotic string theories in uncompactified dimensions < 10. Phys. Lett. B169, 41-46 (1986)
51. [R-S-Z] Ranganathan, K., Sonoda, H., Zwiebach, B.: Connections on the state space over conformal field theories. Nucl. Phys. B414, 405-460 (1994)
52. [R-R-S] Recknagel, A., Roggenkamp, D., Schomerus, V.: On relevant boundary perturbations of unitary minimal models. Nucl. Phys. B588, 552-564 (2000)
53. [Re] Rennie, A.: Commutative geometries are spin manifolds. Rev. Math. Phys. 13(4), 409-464 (2001)
54. [R-W1] Runkel, I., Watts, G.M.T.: A non-rational CFT with c = 1 as a limit of minimal models. In: Proceedings of the Workshop on the Quantum Structure of Spacetime and the Geometric Nature of Fundamental Interactions, Corfu, Greece, 13-20 September 2001 http://arxiv/org/ abs/hep-th/0107118. 2001
55. [R-W2] Runkel, I., Watts, G.M.T.: A non-rational CFT with central charge 1. Fortsch. Phys. 50, 959-965 (2002)
56. [Sch] Schwinger, J.: The theory of quantized fields. II. In: Schwinger, J. (ed): Selected papers on quantum electrodynamics. New York: Dover Publications Inc., 1958, pp. 356-371
57. [S-Y-Z] Strominger, A., Yau, S.-T., Zaslow, E.: Mirror symmetry is T-duality. Nucl. Phys. B479, 243-259 (1996)
58. [V-W] Vafa, C., Witten, E.: On orbifolds with discrete torsion. J. Geom. Phys. 15, 189-214 (1995)
59. [Wi] Widder, D.V.: The Laplace Transform. Princeton Mathematical Series, v. 6, Princeton, NJ: Princeton University Press, 1941
60. [Za1] Zamolodchikov, A.B.: Conformal symmetry and multicritical points in two-dimensional quantum field theory. Sov. J. Nucl. Phys. 44, 529-533 (1986), in Russian; reprinted in [I-S-Z]
61. [Za2] Zamolodchikov, A.B.: Renormalization group and perturbation theory near fixed points in two-dimensional field theory. Sov. J. Nucl. Phys. 46, 1090-1096 (1987)
62. [Zh] Zhu, Y.: Modular invariance of characters of vertex operator algebras. J. Am. Math. Soc. 9, 237-302 (1996)