Modular bootstrap for boundary N = 2 Liouville theory

Journal of High Energy Physics

Volumn 8, Issue 1, 2004, Pages 653-700

  Eguchi, Tohru ^a   Sugawara, Yuji ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

Conformal Field Models in String Theory; D branes; Superstring Vacua; Superstrings and Heterotic Strings

Indexed keywords

EID: 23144449184     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2004/01/025     Document Type: Article

References (88)

1. D. Kutasov and N. Seiberg, Noncritical superstrings, Phys. Lett. B 251 (1990) 67;
2. D. Kutasov, Some properties of (non)critical strings, hep-th/9110041.
3. V. Eateev, A.B. Zainolodchikov and A.B. Zainolodchikov, Boundary liouville field theory. I: Boundary state and boundary two-point function, hep-th/0001012.
4. J. Teschner, Remarks on Liouville theory with boundary, hep-th/0009138.
5. A.B. Zainolodchikov and A.B. Zainolodchikov, Liouville field theory on a pseudosphere, hep-th/0101152.
6. T. Fukuda and K. Hosomichi, Super Liouville theory with boundary, Nucl. Phys. B 635 (2002) 215 [hep-th/0202032].
7. C. Ahn, C. Rim and M. Stanishkov, Exact one-point function of N = 1 super-Liouville theory with boundary, Nucl. Phys. B 636 (2002) 497 [hep-th/0202043].
8. D. Ghoshal and C. Vafa, C = 1 string as the topological theory of the conifold, Nucl. Phys. B 453 (1995) 121 [hep-th/9506122].
9. H. Ooguri and C. Vafa, Two-dimensional black hole and singularities of CY manifolds, Nucl. Phys. B 463 (1996) 55 [hep-th/9511164].
10. O. Aharony, M. Berkooz, D. Kutasov and N. Seiberg, Linear dilatons, NS5-branes and holography, J. High Energy Phys. 10 (1998) 004 [hep-th/9808149].
11. A. Giveon, D. Kutasov and O. Pele, Holography for non-critical superstrings, J. High Energy Phys. 10 (1999) 035 [hep-th/9907178].
12. A. Giveon and D. Kutasov, Little string theory in a double scaling limit, J. High Energy Phys. 10 (1999) 034 [hep-th/9909110];
13. Comments on double scaled little string theory, J. High Energy Phys. 01 (2000) 023 [hep-th/9911039].
14. O. Pelc, Holography, singularities on orbifolds and 4d N = 2 SQCD, J. High Energy Phys. 03 (2000) 012 [hep-th/0001054].
15. T. Eguchi and Y. Sugawara, Modular invariance in superstring on Calabi-Yau n-fold with A-D-E singularity, Nucl. Phys. B 577 (2000) 3 [hep-th/0002100].
16. S. Mizoguchi, Modular invariant critical superstrings on four-dimensional minkowski space x two-dimensional black hole, J. High Energy Phys. 04 (2000) 014 [hep-th/0003053].
17. S. Yamaguchi, Gepner-like description of a string theory on a non-compact singular Calabi-Yau manifold, Nucl. Phys. B 594 (2001) 190 [hep-th/0007069];
18. Noncompact gepner models with discrete spectra, Phys. Lett. B 509 (2001) 346 [hep-th/0102176];
19. Coset character identities in superstring compactifications, J. High Energy Phys. 01 (2002) 023 [hep-th/0112004].
20. M. Naka and M. Nozaki, Singular Calabi-Yau manifolds and ADE classification of CFT's, Nucl. Phys. B 599 (2001) 334 [hep-th/0010002].
21. K. Hori and A. Kapustin, Worldsheet descriptions of wrapped NS five-branes, J. High Energy Phys. 11 (2002) 038 [hep-th/0203147].
22. W. Lerche, On a boundary CFT description of nonperturbative N = 2 Yang-Mills theory, hep-th/0006100.
23. W. Lerche, C.A. Lutken and C. Schweigert, D-branes on ALE spaces and the ADE classification of conformal field theories, Nucl. Phys. B 622 (2002) 269 [hep-th/0006247].
24. T. Eguchi and Y. Sugawara, D-branes in singular Calabi-Yau n-fold and N = 2 Liouville theory, Nucl. Phys. B 598 (2001) 467 [hep-th/0011148].
25. J. McGreevy and H. Verlinde, Strings from tachyons: the c = 1 matrix reloaded, J. High Energy Phys. 12 (2003) 054 [hep-th/0304224].
26. I.R. Klebanov, J. Maldacena and N. Seiberg, D-brane decay in two-dimensional string theory, J. High Energy Phys. 07 (2003) 045 [hep-th/0305159].
27. J. McGreevy, J. Teschner and H. Verlinde, Classical and quantum D-branes in 2D string theory, hep-th/0305194.
28. E.J. Martinec, The annular report on non-critical string theory, hep-th/0305148.
29. S.Y. Alexandrov, V.A. Kazakov and D. Kutasov, Non-perturbative effects in matrix models and D-branes, J. High Energy Phys. 09 (2003) 057 [hep-th/0306177].
30. T. Takayanagi and N. Toumbas, A matrix model dual of type-0B string theory in two dimensions, J. High Energy Phys. 07 (2003) 064 [hep-th/0307083].
31. M.R. Douglas et al., A new hat for the c = 1 matrix model, hep-th/0307195.
32. D. Gaiotto, N. Itzhaki and L. Rastelli, On the bCFT description of holes in the c = 1 matrix model, Phys. Lett. B 575 (2003) 111 [hep-th/0307221].
33. M. Gutperle and P. Kraus, D-brane dynamics in the c = 1 matrix model, hep-th/0308047.
34. A. Sen, Open-closed duality: lessons from matrix model, hep-th/0308068.
35. J. McGreevy, S. Murthy and H. Verlinde, Two-dimensional superstrings and the supersymmetric matrix model, hep-th/0308105.
36. A. Kapustin, Noncritical superstrings in a Ramond-Ramond background, hep-th/0308119.
37. A. Giveon, A. Konechny, A. Pakman and A. Sever, Type-0 strings in a 2-d black hole, J. High Energy Phys. 10 (2003) 025 [hep-th/0309056].
38. J.L. Karczmarek and A. Strominger, Matrix cosmology, hep-th/0309138.
39. O. DeWolfe, R. Roiban, M. Spradlin, A. Volovich and J. Walcher, On the S-matrix of type 0 string theory, J. High Energy Phys. 11 (2003) 012 [hep-th/0309148].
40. I.R. Klebanov, J. Maldacena and N. Seiberg, Unitary and complex matrix models as 1-d type 0 strings, hep-th/0309168.
41. S. Dasgupta and T. Dasgupta, Renormalization group approach to c = 1 matrix model on a circle and D-brane decay, hep-th/0310106.
42. S. Alexandrov, (m,n) ZZ branes and the c = 1 matrix model, hep-th/0310135.
43. J. Gomis and A. Kapustin, Two-dimensional unoriented strings and matrix models, hep-th/0310195.
44. S. Mukhi, Topological matrix models, Liouville matrix model and c = 1 string theory, hep-th/0310287.
45. O. Bergman and S. Hirano, The cap in the hat: unoriented 2D strings and matrix(- vector) models, hep-th/0311068.
46. W. Boucher, D. Friedan and A. Kent, Determinant formulae and unitarity for the N = 2 superconformal algebras in two-dimensions or exact results on string compactification, Phys. Lett. B 172 (1986) 316.
47. V.K. Dobrev, Characters of the unitarizable highest weight modules over the N = 2 superconformal algebras, Phys. Lett. B 186 (1987) 43.
48. T. Eguchi and A. Taormina, Character formulas for the N = 4 superconformal algebra, Phys. Lett. B 200 (1988) 315;
49. On the unitary representations of N = 2 and N = 4 superconformal algebras, Phys. Lett. B 210 (1988) 125.
50. T. Eguchi, H. Ooguri, A. Taormina and S.-K. Yang, Superconformal algebras and string compactification on manifolds with SU(N) holonomy, Nucl. Phys. B 315 (1989) 193.
51. S. Odake, Extension of N = 2 superconformal algebra and Calabi-Yau compactification, Mod. Phys. Lett. A 4 (1989) 557;
52. Character formulas of an extended superconformal algebra relevant to string compactification, Int. J. Mod. Phys. A 5 (1990) 897.
53. Y. Hikida and Y. Sugawara, Superstring vacua of 4-dimensional PP-waves with enhanced supersymmetry, J. High Energy Phys. 10 (2002) 067 [hep-th/0207124].
54. K. Miki, The representation theory of the SO(3) invariant superconformal algebra, Int. J. Mod. Phys. A 5 (1990) 1293.
55. N. Ishibashi, The boundary and crosscap states in conformal field theories, Mod. Phys. Lett. A 4 (1989) 251.
56. J.L. Cardy, Boundary conditions, fusion rules and the verlinde formula, Nucl. Phys. B 324 (1989) 581.
57. H. Ooguri, Y. Oz and Z. Yin, D-branes on Calabi-Yau spaces and their mirrors, Nucl. Phys. B 477 (1996) 407 [hep-th/9606112].
58. P. Baseilhac and V.A. Fateev, Expectation values of local fields for a two-parameter family of integrable models and related perturbed conformal field theories, Nucl. Phys. B 532 (1998) 567 [hep-th/9906010].
59. C. Ahn, C. Kim, C. Rim and M. Stanishkov, Duality in N = 2 super-Liouville theory, hep-th/0210208.
60. J. Teschner, On the Liouville three point function, Phys. Lett. B 363 (1995) 65 [hep-th/9507109].
61. N. Seiberg, Notes on quantum Liouville theory and quantum gravity, Prog. Theor. Phys. Suppl. 102 (1990) 319.
62. C.-r. Ahn and M. Yamamoto, Boundary action of N = 2 super-Liouville theory, hep-th/0310046.
63. A. Recknagel and V. Schomerus, D-branes in Gepner models, Nucl. Phys. B 531 (1998) 185 [hep-th/9712186].
64. Y. Hikida, M. Nozaki and Y. Sugawara, Formation of spherical D2-brane from multiple dO-branes, Nucl. Phys. B 617 (2001) 117 [hep-th/0101211].
65. A. Maloney, A. Strominger and X. Yin, S-brane thermodynamics, J. High Energy Phys. 10 (2003) 048 [hep-th/0302146].
66. M. Gutperle and A. Strominger, Spacelike branes, J. High Energy Phys. 04 (2002) 018 [hep-th/0202210].
67. A. Sen, Rolling tachyon, J. High Energy Phys. 04 (2002) 048 [hep-th/0203211];
68. Tachyon matter, J. High Energy Phys. 07 (2002) 065 [hep-th/0203265];
69. Field theory of tachyon matter, Mod. Phys. Lett. A 17 (2002) 1797 [hep-th/0204143].
70. A. Strominger, Open string creation by S-branes, hep-th/0209090.
71. N. Lambert, H. Liu and J. Maldacena, Closed strings from decaying D-branes, hep-th/0303139.
72. A. Sen, Non-BPS states and branes in string theory, hep-th/9904207.
73. Y. Sugawara, Thermal partition functions for S-branes, J. High Energy Phys. 08 (2003) 008 [hep-th/0307034].
74. J.J. Atick and E. Witten, The hagedorn transition and the number of degrees of freedom of string theory, Nucl. Phys. B 310 (1988) 291.
75. E. Marinari and G. Parisi, The supersymmetric one-dimensional string, Phys. Lett. B 240 (1990) 375.
76. P. Di Francesco and D. Kutasov, World sheet and space-time physics in two-dimensional (super)string theory, Nucl. Phys. B 375 (1992) 119 [hep-th/9109005].
77. V. Kazakov, I.K. Rostov and D. Kutasov, A matrix model for the two-dimensional black hole, Nucl. Phys. B 622 (2002) 141 [hep-th/0101011].
78. F. Larsen, A. Naqvi and S. Terashima, Rolling tachyons and decaying branes, J. High Energy Phys. 02 (2003) 039 [hep-th/0212248].
79. K. Hori and A. Kapustin, Duality of the fermionic 2d black hole and N = 2 Liouville theory as mirror symmetry, J. High Energy Phys. 08 (2001) 045 [hep-th/0104202].
80. V. Fateev, A. B. Zamolodchikov and A. B. Zamolodchikov, unpublished, as cited in [69].
81. M. Gutperle and A. Strominger, Timelike boundary Liouville theory, Phys. Rev. D 67 (2003) 126002 [hep-th/0301038].
82. A. Strominger and T. Takayanagi, Correlators in timelike bulk Liouville theory, Adv. Theor. Math. Phys. 7 (2003) 369 [hep-th/0303221].
83. V. Schomerus, Rolling tachyons from Liouville theory, J. High Energy Phys. 11 (2003) 043 [hep-th/0306026].
84. S. Ribault and V. Schomerus, Branes in the 2D black hole, hep-th/0310024.
85. 3, J. High Energy Phys. 02 (2002) 016 [hep-th/0112198].
86. 3, Nucl. Phys. B 615 (2001) 133 [hep-th/0106005].
87. 3, Nucl. Phys. B 632 (2002) 283 [hep-th/0112188].
88. A.M. Semikhatov, I.Y. Tipunin and A. Taormina, Higher-level Appell functions, modular transformations, and characters, math.QA/0311314.