Fusion rules and boundary conditions in the c = 0 triplet model

Journal of Physics A: Mathematical and Theoretical

Volumn 42, Issue 32, 2009, Pages

  Gaberdiel, Matthias R ^a   Runkel, Ingo ^b   Wood, Simon ^a  

^a ETH ZURICH   (Switzerland)

^b KING'S COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70449584994     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/42/32/325403     Document Type: Article

References (76)

1. Jeng M, Piroux G and Ruelle P 2006 Height variables in the Abelian sandpile model: scaling fields and correlations J. Stat. Mech. P10015 (arXiv:cond-mat/0609284)
2. Pearce P A and Rasmussen J 2007 Solvable critical dense polymers J. Stat. Mech. P02015 (arXiv:hep-th/0610273)
3. Read N and Saleur H 2007 Associative-algebraic approach to logarithmic conformal field theories Nucl. Phys. B 777 316 (arXiv:hep-th/0701117)
4. Ruelle P 2007 Wind on the boundary for the Abelian sandpile model J. Stat. Mech. P09013 (arXiv:0707.3766 [cond-mat.stat-mech])
5. Mathieu P and Ridout D 2007 From percolation to logarithmic conformal field theory Phys. Lett. B 657 120 (arXiv:0708.0802 [hep-th])
6. Rasmussen J and Pearce P A 2008 W-extended fusion algebra of critical percolation J. Phys. A: Math. Theor. 41 295208 (arXiv:0804.4335 [hep-th])
7. Ridout D 2009 On the percolation BCFT and the crossing probability of Watts Nucl. Phys. B 810 503 (arXiv:0808.3530 [hep-th])
8. Saint-Aubin Y, Pearce P A and Rasmussen J 2009 Geometric exponents, SLE and logarithmic minimal models J. Stat. Mech. P02028 (arXiv:0809.4806 [cond-mat.stat-mech])
9. Nigro A 2009 Integrals of motion for critical dense polymers and symplectic fermions arXiv:0903.5051 [hep-th]
10. Grumiller D and Johansson N 2009 Consistent boundary conditions for cosmological topologically massive gravity at the chiral point Int. J. Mod. Phys. D 17 2367 (arXiv:0808.2575 [hep-th])
11. Maloney A, Song W and Strominger A 2009 Chiral gravity, log gravity and extremal CFT arXiv:0903.4573 [hep-th]
12. Gurarie V and Ludwig A W W 2002 Conformal algebras of 2D disordered systems J. Phys. A: Math. Gen. 35 L377 (arXiv:cond-mat/9911392)
13. Gaberdiel M R and Kausch H G 1996 A rational logarithmic conformal field theory Phys. Lett. B 386 131 (arXiv:hep-th/9606050)
14. Fuchs J, Hwang S, Semikhatov A M and Tipunin I Y 2004 Nonsemisimple fusion algebras and the Verlinde formula Commun. Math. Phys. 247 713 (arXiv:hep-th/0306274)
15. 2-cofiniteness for a family of W-algebras J. Phys. A: Math. Gen. 39 951 (arXiv:math-ph/0508015)
16. Gaberdiel M R and Runkel I 2008 From boundary to bulk in logarithmic CFT J. Phys. A: Math. Theor. 41 075402 (arXiv:0707.0388 [hep-th])
17. Adamovic D and Milas A 2008 On the triplet vertex algebra W(p) Adv. Math. 217 2664 (arXiv:0707.1857 [math.QA])
18. Feigin B L, Gainutdinov A M, Semikhatov A M and Tipunin I Y 2006 Logarithmic extensions of minimal models: characters and modular transformations Nucl. Phys. B 757 303 (arXiv:hep-th/0606196)
19. Rasmussen J 2009 W-extended logarithmic minimal models Nucl. Phys. B 807 495 (arXiv:0805.2991 [hep-th])
20. Eberle H and Flohr M 2006 Virasoro representations and fusion for general augmented minimal models J. Phys. A: Math. Gen. 39 15245 (arXiv:hep-th/0604097)
21. Rasmussen J 2008 Polynomial fusion rings of W-extended logarithmic minimal models arXiv:0812.1070 [hep-th]
22. Ruelle P 2002 A c = -2 boundary changing operator for the Abelian sandpile model Phys. Lett. B 539 172 (arXiv:hep-th/0203105)
23. Piroux G and Ruelle P 2004 Pre-logarithmic and logarithmic fields in sandpile model J. Stat. Mech. P10005 (arXiv:hep-th/0407143)
24. Piroux G and Ruelle P 2005 Logarithmic scaling for height variables in the Abelian sandpile model Phys. Lett. B 607 188 (arXiv:cond-mat/0410253)
25. Izmailian N S, Priezzhev V B, Ruelle P and Hu C K 2005 Logarithmic conformal field theory and boundary effects in the dimer model Phys. Rev. Lett. 95 260602 (arXiv:cond-mat/0512703)
26. Pearce P A, Rasmussen J and Zuber J-B 2006 Logarithmic minimal models J. Stat. Mech. P11017 (arXiv:hep-th/0607232)
27. Pearce P A, Rasmussen J and Ruelle P 2008 Integrable boundary conditions and W-extended fusion in the logarithmic minimal models LM(1,p) J. Phys. A: Math. Gen. 41 295201 (arXiv:0803.0785 [hep-th])
28. Creutzig T, Quella T and Schomerus V 2008 Branes in the GL(1|1) WZNW-model Nucl. Phys. B 792 257 (arXiv:0708.0583 [hep-th])
29. Quella T, Schomerus V and Creutzig T 2008 Boundary spectra in superspace sigma-models J. High Energy Phys. JHEP 10(2008)024 (arXiv:0712.3549 [hep-th])
30. Creutzig T and Schomerus V 2009 Boundary correlators in supergroup WZNW models Nucl. Phys. B 807 471 (arXiv:0804.3469 [hep-th])
31. Creutzig T 2009 Geometry of branes on supergroups Nucl. Phys. B 812 301 (arXiv:0809.0468 [hep-th])
32. Mitev V, Quella T and Schomerus V 2008 Principal chiral model on superspheres J. High Energy Phys. JHEP 11(2008)086 (arXiv:0809.1046 [hep-th])
33. Creutzig T and Ronne P B 2008 The GL(1|1)-symplectic fermion correspondence arXiv:0812.2835 [hep-th]
34. Kogan I I and Wheater J F 2000 Boundary logarithmic conformal field theory Phys. Lett. B 486 353 (arXiv:hep-th/0003184)
35. Ishimoto Y 2001 Boundary states in boundary logarithmic CFT Nucl. Phys. B 619 415 (arXiv:hep-th/0103064)
36. Kawai S and Wheater J F 2001 Modular transformation and boundary states in logarithmic conformal field theory Phys. Lett. B 508 203 (arXiv:hep-th/ 0103197)
37. Bredthauer A and Flohr M 2002 Boundary states in c = -2 logarithmic conformal field theory Nucl. Phys. B 639 450 (arXiv:hep-th/0204154)
38. Bredthauer A 2003 Boundary states and symplectic fermions Phys. Lett. B 551 378 (arXiv:hep-th/0207181)
39. Ishimoto Y 2004 Two-point functions and logarithmic boundary operators in boundary logarithmic conformal field theories J. High Energy Phys. JHEP 08 (2004)039 (arXiv:hep-th/0405237)
40. Gaberdiel M R and Runkel I 2006 The logarithmic triplet theory with boundary J. Phys. A: Math. Gen. 39 14745 (arXiv:hep-th/0608184)
41. Creutzig T, Quella T and Schomerus V 2008 New boundary conditions for the c = -2 ghost system Phys. Rev. D 77 026003 (arXiv:hep-th/0612040)
42. Gainutdinov A M and Tipunin I Y 2007 Radford, Drinfeld, and Cardy boundary states in (1,p) logarithmic conformal field models arXiv:0711.3430 [hep-th]
43. Runkel I 1999 Boundary structure constants for the A-series Virasoro minimal models Nucl. Phys. B 549 563 (arXiv:hep-th/9811178)
44. Felder G, Fröhlich J, Fuchs J and Schweigert C 2002 Correlation functions and boundary conditions in RCFT and three-dimensional topology Compos. Math. 131 189 (arXiv:hep-th/9912239)
45. Fuchs J, Runkel I and Schweigert C 2002 TFT construction of RCFT correlators: I. Partition functions Nucl. Phys. B 646 353 (arXiv:hep-th/0204148)
46. Fjelstad J, Fuchs J, Runkel I and Schweigert C 2008 Uniqueness of open/closed rational CFT with given algebra of open states Adv. Theor. Math. Phys. 12 1283 (arXiv:hep-th/0612306)
47. Kong L and Runkel I 2007 Cardy algebras and sewing constraints: I arXiv:0708.1897 [math.QA]
48. Kong L and Runkel I 2008 Morita classes of algebras in modular tensor categories Adv. Math. 219 1548 (arXiv:0708.1897 [math.CT])
49. Cardy J L 1989 Boundary conditions, fusion rules and the Verlinde formula Nucl. Phys. B 324 581
50. Gaberdiel M R and Kausch H G 1999 A local logarithmic conformal field theory Nucl. Phys. B 538 631 (arXiv:hep-th/9807091)
51. Adamovic D and Milas A 2009 Lattice construction of logarithmic modules for certain vertex algebras arXiv:0902.3417 [math.QA]
52. Nahm W 1994 Quasirational fusion products Int. J. Mod. Phys. B 8 3693 (arXiv:hep-th/9402039)
53. Gaberdiel M R and Kausch H G 1996 Indecomposable fusion products Nucl. Phys. B 477 293 (arXiv:hep-th/9604026)
54. Fuchs J 2007 On non-semisimple fusion rules and tensor categories Contemp. Math. 442 315 (arXiv:hep-th/0602051)
55. Wang W 1993 Rationality of Virasoro vertex operator algebras Int. Math. Res. Not. 7 197
56. Joyal A and Street R 1993 Braided tensor categories Adv. Math. 102 20
57. Bakalov B and Kirillov A A 2001 Lectures on Tensor Categories and Modular Functors (Providence, RI: American Mathematical Society)
58. Huang Y-Z 1996 Virasoro vertex operator algebras, the (nonmeromorphic) operator product expansion and the tensor product theory J. Alg. 182 201 (arXiv:q-alg/9505020)
59. Huang Y-Z 2008 Rigidity and modularity of vertex tensor categories Commun. Contemp. Math. 10 871 (arXiv:math/0502533)
60. Kausch H G 1991 Extended conformal algebras generated by a multiplet of primary fields Phys. Lett. B 259 448
61. Huang Y Z, Lepowsky J and Zhang L 2007 Logarithmic tensor product theory for generalized modules for a conformal vertex algebra arXiv:0710.2687 [math.QA]
62. Huang Y-Z 2007 Cofiniteness conditions, projective covers and the logarithmic tensor product theory arXiv:0712.4109 [math.QA]
63. Huang Y-Z 2009 Representations of vertex operator algebras and braided finite tensor categories arXiv:0903.4233 [math.QA]
64. Cardy J L 1984 Conformal invariance and surface critical behavior Nucl. Phys. B 240 514
65. Cardy J L and Lewellen D C 1991 Bulk and boundary operators in conformal field theory Phys. Lett. B 259 274
66. Lewellen D C 1992 Sewing constraints for conformal field theories on surfaces with boundaries Nucl. Phys. B 372 654
67. Behrend R E, Pearce P A, Petkova V B and Zuber J-B 2000 Boundary conditions in rational conformal field theories Nucl. Phys. B 570 525
68. Behrend R E, Pearce P A, Petkova V B and Zuber J-B 2000 Boundary conditions in rational conformal field theories Nucl. Phys. B 579 707 (arXiv:hep-th/9908036)
69. Semikhatov A M 2007 A note on the logarithmic (p, p′) fusion arXiv:0710.5157 [hep-th]
70. Gaberdiel M R 1994 Fusion in conformal field theory as the tensor product of the symmetry algebra Int. J. Mod. Phys. A 9 4619 (arXiv:hep-th/9307183)
71. Rohsiepe F 1996 On reducible but indecomposable representations of the Virasoro algebra arXiv:hep-th/9611160
72. Kytölä K and Ridout D 2009 On staggered indecomposable Virasoro modules arXiv:0905.0108 [math-ph]
73. Lane S Mac 1998 Categories for the Working Mathematician 2nd edn (Berlin: Springer)
74. Majid S 2000 Foundations of Quantum Group Theory (Cambridge: Cambridge University Press)
75. Ostrik V 2003 Module categories, weak Hopf algebras and modular invariants Transform. Groups 8 177 (arXiv:math/0111139)
76. Quella T and Schomerus V 2007 Free fermion resolution of supergroup WZNW models J. High Energy Phys. JHEP 09(2007)085 (arXiv:0706.0744 [hep-th])