Virasoro representations and fusion for general augmented minimal models

Journal of Physics A: Mathematical and General

Volumn 39, Issue 49, 2006, Pages 15245-15286

  Eberle, Holger ^a   Flohr, Michael ^a  

^a UNIVERSITY OF BONN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33846631309     PISSN: 03054470     EISSN: 13616447     Source Type: Journal    
DOI: 10.1088/0305-4470/39/49/012     Document Type: Article

References (57)

1. Saleur H 1992 Polymers and percolation in two dimensions and twisted N = 2 supersymmetry Nucl. Phys. B 382 486-531 (Preprint hep-th/9111007)
2. Gurarie V, Flohr M and Nayak C 1997 The Haldane-Rezayi quantum Hall state and conformal field theory Nucl. Phys. B 498 513-38 (Preprint cond-mat/9701212)
3. Ruelle P 2002 A c = -2 boundary changing operator for the Abelian sandpile model Phys. Lett. B 539 172-7 (Preprint hep-th/0203105)
4. Pearce P A, Rittenberg V and de Gier J 2001 Critical Q = 1 Potts model and Temperley-Lieb stochastic processes Preprint cond-mat/0108051
5. Gravanis E and Mavromatos N E 2001 Impulse action on D-particles in Robertson-Walker space times, higher-order logarithmic conformal algebras and cosmological horizons Preprint hep-th/0106146
6. Bakas I and Sfetsos K 2002 PP-waves and logarithmic conformal field theories Nucl. Phys. B 639 223-40 (Preprint hep-th/0205006)
7. Lambert N, Liu H and Maldacena J 2003 Closed strings from decaying D-branes Preprint hep-th/0303139
8. Flohr M A I 2004 Logarithmic conformal field theory or how to compute a torus amplitude on the sphere From Fields to Strings vol 2 ed M Shifman pp 1201-56 (Preprint hep-th/0407003)
9. Flohr M 2003 Bits and pieces in logarithmic conformal field theory Int. J. Mod. Phys. A 18 4497-592 (Preprint hep-th/0111228)
10. Gaberdiel M R 2003 An algebraic approach to logarithmic conformal field theory Int. J. Mod. Phys. A 18 4593-638 (Preprint hep-th/0111260)
11. Kawai S 2003 Logarithmic conformal field theory with boundary Int. J. Mod. Phys. A 18 4655-84 (Preprint hep-th/0204169)
12. k logarithmic conformal field theories PhD Thesis University of Oxford Preprint hep-th/0210070
13. Flohr M and Gaberdiel M R 2006 Logarithmic torus amplitudes J. Phys. A: Math. Gen. 39 1955-68 (Preprint hep-th/0509075)
14. Flohr M A I 1998 Singular vectors in logarithmic conformal field theories Nucl. Phys. B 514 523-52 (Preprint hep-th/9707090)
15. Flohr M 2000 Null vectors in logarithmic conformal field theory Preprint hep-th/0009137
16. Flohr M 2002 Operator product expansion in logarithmic conformal field theory Nucl. Phys. B 634 511-45 (Preprint hep-th/0107242)
17. Flohr M and Krohn M 2006 Four-point functions in logarithmic conformal field theories Nucl. Phys. B 743 276-306 (Preprint hep-th/0504211)
18. Moghimi-Araghi S, Rouhani S and Saadat M 2001 Logarithmic conformal field theory through nilpotent conformal dimensions Nucl. Phys. B 599 531-46 (Preprint hep-th/0008165)
19. Moghimi-Araghi S, Rouhani S and Saadat M 2003 Use of nilpotent weights in logarithmic conformal field theories Int. J. Mod. Phys. A 18 4747-70 (Preprint hep-th/0201099)
20. Gaberdiel M R and Kausch H G 1996 Indecomposable fusion products Nucl. Phys. B 477 293-318 (Preprint hep-th/9604026)
21. Gaberdiel M R and Kausch H G 1996 A rational logarithmic conformal field theory Phys. Lett. B 386 131-7 (Preprint hep-th/9606050)
22. Rohsiepe F 1996 On reducible but indecomposable representations of the Virasoro algebra Preprint hep-th/9611160
23. Gaberdiel M R and Kausch H G 1999 A local logarithmic conformal field theory Nucl. Phys. B 538 631-58 (Preprint hep-th/9807091)
24. Flohr M A I 1996 On modular invariant partition functions of conformal field theories with logarithmic operators Int. J. Mod. Phys. A 11 4147-72 (Preprint hep-th/9509166)
25. Flohr M A I 1997 On fusion rules in logarithmic conformal field theories Int. J. Mod. Phys. A 12 1943-58 (Preprint hep-th/9605151)
26. Kausch H G 1991 Extended conformal algebras generated by a multiplet of primary fields Phys. Lett. B 259 448-55
27. Eberle H, Flohr M and Nichols A (in preparation)
28. 2-cofiniteness for a family of -algebras J. Phys. A: Math. Gen. 39 951-66 (Preprint math-ph/0508015)
29. Feigin B L, Gainutdinov A M, Semikhatov A M and Tipunin I Y 2006 Modular group representations and fusion in logarithmic conformal field theories and in the quantum group center Commun. Math. Phys. 265 47-93 (Preprint hep-th/0504093)
30. Feigin B L, Gainutdinov A M, Semikhatov A M and Tipunin I Y 2005 Kazhdan-Lusztig correspondence for the representation category of the triplet -algebra in logarithmic conformal field theory Preprint math.qa/0512621
31. Flohr M and Müller-Lohmann A 2006 Notes on non-trivial and logarithmic CFTs with c = 0 J. Stat. Mech. 0604 P002 (Preprint hep-th/0510096)
32. Eberle H and Flohr M 2006 Notes on generalised nullvectors in logarithmic CFT Nucl. Phys. B 741 441-66 (Preprint hep-th/0512254)
33. Caux J S, Kogan I I and Tsvelik A M 1996 Logarithmic operators and hidden continuous symmetry in critical disordered models Nucl. Phys. B 466 444-62 (Preprint hep-th/9511134)
34. Maassarani Z and Serban D 1997 Non-unitary conformal field theory and logarithmic operators for disordered systems Nucl. Phys. B 489 603-25 (Preprint hep-th/9605062)
35. Ghezelbash A M and Karimipour V 1997 Global conformal invariance in D dimensions and logarithmic correlation functions Phys. Lett. B 402 282-9 (Preprint hep-th/9704082)
36. Rasmussen J 2004 Jordan cells in logarithmic limits of conformal field theory Preprint hep-th/0406110
37. Rasmussen J 2005 On conformal Jordan cells of finite and infinite rank Lett. Math. Phys. 73 83-90 (Preprint hep-th/0408029)
38. Felder G, Fröhlich J and Keller G 1989 Braid matrices and structure constants for minimal conformal models Commun. Math. Phys. 124 647-64
39. Felder G, Fröhlich J and Keller G 1990 On the structure of unitary conformal field theory: II. Representation theoretic approach Commun. Math. Phys. 130 1
40. Gaberdiel M 1994 Fusion in conformal field theory as the tensor product of the symmetry algebra Int. J. Mod. Phys. A 9 4619-36 (Preprint hep-th/9307183)
41. Lepowsky J 2005 From the representation theory of vertex operator algebras to modular tensor categories in conformal field theory Proc. Natl. Acad. Sci. 102 5304-5 (Preprint math.qa/0504311)
42. Schweigert C, Fuchs J and Runkel I 2006 Categorification and correlation functions in conformal field theory Preprint math.ct/0602079
43. Nahm W 1994 Quasirational fusion products Int. J. Mod. Phys. B 8 3693-702 (Preprint hep-th/9402039)
44. Gaberdiel M 1994 Fusion rules of chiral algebras Nucl. Phys. B 417 130-150 (Preprint hep-th/9309105)
45. Bauer C, Frink A and Kreckel R 2002 Introduction to the GiNaC framework for symbolic computation within the C++ programming language J. Symbolic Comput. 33 1 (Preprint cs.sc/0004015) (the GiNaC library is available at http://www.ginac.de)
46. Belavin A A, Polyakov A M and Zamolodchikov A B 1984 Infinite conformal symmetry in two-dimensional quantum field theory Nucl. Phys. B 241 333-80
47. Francesco P D, Mathieu P and Senechal D 1997 Conformal Field Theory (New York: Springer)
48. Feigin B L and Fuks D B 1983 Verma modules over the Virasoro algebra Funct. Anal. Appl. 17 241-2
49. Rocha-Caridi A 1985 Vacuum vector representations of the Virasoro algebra Vertex Operators in Mathematics and Physics ed J Lepowsky (Berlin: Springer) p 451
50. Eberle H 2006 Conformal field theory between supersymmetry and indecomposable structures PhD Thesis University of Bonn
51. Watts G M T 1996 A crossing probability for critical percolation in two dimensions J. Phys. A: Math. Gen. 29 L363 (Preprint cond-mat/9603167)
52. Cardy J 2001 Lectures on conformal invariance and percolation Preprint math-ph/0103018
53. Flohr M A I and Müller-Lohmann A 2005 Conformal field theory properties of two-dimensional percolation J. Stat. Mech. 0512 P004 (Preprint hep-th/0507211)
54. Gurarie V and Ludwig A W W 2002 Conformal algebras of 2D disordered systems J. Phys. A: Math. Gen. 35 L377-84 (Preprint cond-mat/9911392)
55. Gurarie V and Ludwig A W W 2004 Conformal field theory at central charge c = 0 and two dimensional critical systems with quenched disorder From Fields to Strings vol 2 ed M Shifman pp 1384-440 (Preprint hep-th/0409105)
56. Minahan J A and Zarembo K 2003 The Bethe-ansatz for N = 4 super Yang-Mills J. High Energy Phys. JHEP03(2003)013 (Preprint hep-th/0212208)
57. Beisert N, Dippel V and Staudacher M 2004 A novel long range spin chain and planar N = 4 super Yang-Mills J. High Energy Phys. JHEP07(2004)075 (Preprint hep-th/0405001)