Irrational conformal field theory

Physics Report

Volumn 265, Issue 1-2, 1996, Pages 1-138

  Halpern, M B ^a   Kiritsis, E ^b   Obers, N A ^c   Clubok, K ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b CERN   (Switzerland)

^c CENTRE DE PHYSIQUE THÉORIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030077767     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/0370-1573(95)00017-8     Document Type: Review

References (187)

1. [1] M. Ademollo et al., Phys. Lett. B 62 (1976) 105.
2. [2] M. Ademollo et al., Nucl. Phys. B 111 (1976) 77.
3. [3] V. Aldaya and J. Navarro-Salas, Commun. Math. Phys. 113 (1987) 375.
4. [4] I. Antoniadis, C. Bachas, C. Kounnas and P. Windey, Phys. Lett. B 171 (1986) 51.
5. [5] I. Antoniadis and N.A. Obers, Nucl. Phys. B 423 (1994) 639.
6. [6] F. Bais, P. Bouwknegt, K. Schoutens and M. Surridge, Nucl. Phys. B 304 (1988) 348.
7. [7] F. Bais, P. Bouwknegt, K. Schoutens and M. Surridge, Nucl. Phys. B 304 (1988) 371.
8. [8] I. Bakas, Phys. Lett. B 228 (1989) 57.
9. [9] T. Banks and L. Dixon, Nucl. Phys. B 307 (1988) 93.
10. [10] T. Banks, L. Dixon, D. Friedan and E. Martinec, Nucl. Phys. B 299 (1988) 613.
11. [11] T. Banks, D. Horn and H. Neuberger, Nucl. Phys. B 108 (1976) 119.
12. [12] K. Bardakçi, Nucl. Phys. B 369 (1992) 461.
13. [13] K. Bardakçi, Nucl. Phys. B 391 (1993) 257.
14. [14] K. Bardakçi, Nucl. Phys. B 431 (1994) 191.
15. [15] K. Bardakçi, M. Crescimanno and S.A. Hotes, Nucl. Phys. B 349 (1991) 439.
16. [16] K. Bardakçi, M. Crescimanno and S.A. Hotes, Phys. Lett. B 257 (1991) 313.
17. [17] K. Bardakçi, M. Crescimanno and E. Rabinovici, Nucl. Phys. B 344 (1990) 344.
18. [18] K. Bardakçi and M.B. Halpern, Phys. Rev. D 3 (1971) 2493.
19. [19] K. Bardakçi, E. Rabinovici and B. Säring, Nucl. Phys. B 299 (1988) 151;
20. D. Altschuler, K. Bardakçi and E. Rabinovici, Comm. Math. Phys. 118 (1988) 241.
21. [20] I. Bars, Phys. Lett. B 245 (1990) 35.
22. [21] I. Bars, Nucl. Phys. B 334 (1990) 125.
23. [22] I. Bars, "Strings and Large N QCD", in the proceedings of the International Conference on High Energy Physics, Beyond the Standard Model II, 1990, World Scientific, 1991.
24. [23] A.A. Belavin, A.M. Polyakov and A.B. Zamolodchikov, Nucl. Phys. B 241 (1984) 333.
25. [24] A.A. Belov and Yu.E. Lozovik, JETP Lett. 52 (1990) 576.
26. [25] A.A. Belov and Yu.E. Lozovik, Sov. J. Nucl. Phys. 55 (1992) 307.
27. [26] D. Bernard, Nucl. Phys. B 303 (1988) 77.
28. [27] D. Bernard and G. Felder, Commun. Math. Phys. 127 (1990) 145.
29. [28] J. de Boer, K. Clubok and M.B. Halpern, Int. J. Mod. Phys. A 9 (1994) 2451.
30. [29] P. Bouwknegt and K. Schoutens, Phys. Rep. 223 (1993) 183.
31. [30] P. Bowcock, Nucl. Phys. B 316 (1989) 80.
32. [31] R.C. Brower, Phys. Rev. D 6 (1972) 1655.
33. [32] C.G. Callan, D. Friedan, E.J. Martinec and M.J. Perry, Nucl. Phys. B 262 (1985) 593.
34. [33] K. Clubok and M.B. Halpern, unpublished (1994).
35. [34] R. Cohen and D. Gepner, Mod. Phys. Lett. A 6 (1991) 2249.
36. [35] S. Coleman, Phys. Rev. D 11 (1975) 2088.
37. [36] E. Corrigan and D.B. Fairlie, Nucl. Phys. B 91 (1975) 527.
38. [37] A. Deckmyn and S. Schrans, Phys. Lett. B 274 (1992) 186.
39. [38] A. Deckmyn and W. Troost, Nucl. Phys. B 370 (1992) 231.
40. [39] P.A.M. Dirac, "Lectures on Quantum Mechanics", Belfer Graduate School of Physics, Yeshiva Univ., New York, 1964.
41. [40] J. Distler and H. Kawai, Nucl. Phys. B 321 (1989) 509
42. [41] L.J. Dixon and J. Harvey, unpublished (1989).
43. [42] L.J. Dixon, M.E. Peskin and J. Lykken, Nucl. Phys. B 325 (1989) 329.
44. [43] Vl.S. Dotsenko and V.A. Fateev, Nucl. Phys. B 240 (1984) 312.
45. [44] Vl.S. Dotsenko and V.A. Fateev, Nucl. Phys. B 251 (1985) 691.
46. [45] M.R. Douglas, "G/H Conformal Field Theory", Caltech preprint, CALT-68-1453, 1987.
47. [46] G.V. Dunne, I.G. Halliday and P. Suranyi, Phys. Lett. B 213 (1988) 139.
48. [47] G.V. Dunne, I.G. Halliday and P. Suranyi, Nucl.Phys. B 325 (1989) 526.
49. [48] T. Eguchi and H. Ooguri, Nucl. Phys. B 282 (1987) 308.
50. [49] T. Eguchi and H. Ooguri, Nucl. Phys. B 313 (1989) 492.
51. [50] P. Etingoff, I. Frenkel and A. Kirillov, "Spherical Functions on Affine Lie Groups", Yale preprint, 1994, hep-th/9407047.
52. [51] D.B. Fairlie, as quoted in A. Chodos and C.B. Thorn, Nucl. Phys. B 72 (1974) 509.
53. [52] D.B. Fairlie, P. Fletcher and C.K. Zachos, Phys. Lett. B 218 (1989) 203.
54. [53] D.B. Fairlie, P. Fletcher and C.K. Zachos, J. Math. Phys. 31 (1990) 1088.
55. [54] V.A. Fateev and S.L. Lykyanov, Int. J. Mod. Phys. A 3 (1988) 507.
56. [55] V.A. Fateev and A.B. Zamolodchikov, Nucl. Phys. B 280 (1987) 644.
57. [56] B.L. Feigin and D.B. Fuchs, Funct. Anal. and Appl. 16 (1982) 114.
58. [57] J.M. Figueroa-O'Farrill, Phys. Lett. B 316 (1993) 496.
59. [58] J.M. Figueroa-O'Farrill, "Constructing N=2 Superconformal Algebras out of N=1 Affine Lie Algebras", Bonn preprint, BONN-HE-93/21, hep-th/9308105.
60. [59] J. M. Figueroa-O'Farrill and S. Stanciu, Phys. Lett. B 327 (1994) 40.
61. [60] L. Frappat, E. Ragoucy and F. Thuillier, Phys. Lett. B 262 (1991) 271.
62. [61] J.K. Freericks and M.B. Halpern, Ann. of Phys. 188 (1988) 258; Erratum, ibid. 190 (1989) 212.
63. [62] I.B. Frenkel and V.G. Kač, Inv. Math. 62 (1980) 23.
64. [63] D. Friedan, E. Martinec and S. Shenker, Nucl. Phys. B 271 (1986) 93.
65. [64] D. Friedan, Z. Qiu and S. Shenker, Phys. Lett. B 151 (1985) 37.
66. [65] S. Fubini and G. Veneziano, Nuov. Cim. A 67 (1970) 29.
67. [66] S.J. Gates and O.A. Soloviev, Phys. Lett. B 294 (1992) 342.
68. [67] K. Gawȩdzki and A. Kupiainen, Phys. Lett. B 215 (1988) 119.
69. [68] K. Gawȩdzki and A. Kupiainen, Nucl. Phys. B 320 (1989) 625.
70. [69] M. Gell-Mann and Y. Ne'eman, "The Eightfold Way", W.A. Benjamin, New York, 1964.
71. [70] D. Gepner and Z. Qiu, Nucl. Phys. B 285 (1987) 423.
72. [71] J.L. Gervais and A. Neveu, Nucl. Phys. B 224 (1983) 329.
73. [72] E. Getzler, "Manin Triples and N=2 Superconformal Field Theory", MIT preprint, PRINT-93-0512, hep-th/9307041.
74. [73] A. Giveon, M.B. Halpern, E. Kiritsis and N.A. Obers, Int. J. Mod. Phys. A 7 (1992) 947.
75. [74] A. Giveon, M.B. Halpern, E. Kiritsis and N.A. Obers, Nucl. Phys. B 357 (1991) 655.
76. [75] P. Goddard, A. Kent and D. Olive, Phys. Lett. B 152 (1985) 88.
77. [76] P. Goddard, A. Kent and D. Olive, Commun. Math. Phys. 103 (1986) 105.
78. [77] P. Goddard, D. Olive and G. Waterson, Commun. Math. Phys. 112 (1987) 591.
79. [78] P. Goddard and C.B. Thorn, Phys. Lett. B 40 (1972) 235.
80. [79] A.S. Gorsky and K.G. Selivanov, Mod. Phys. Lett. A 7 (1992) 2601.
81. [80] M.B. Green and J.H. Schwarz, Phys. Lett. B 109 (1982) 444.
82. [81] M.B. Green, J.H. Schwarz and E. Witten, "Superstring Theory", Cambridge University Press, 1987.
83. [82] D. Gross, J.A. Harvey, E. Martinec and R. Rohm, Phys. Rev. Lett. 54 (1985) 502.
84. [83] M.B. Halpern, Phys. Rev. D 4 (1971) 2398.
85. [84] M.B. Halpern, Phys. Rev. D 12 (1975) 1684.
86. [85] M.B. Halpern, Phys. Rev. D 13 (1976) 337.
87. [86] M.B. Halpern, Ann. of Phys. 194 (1989) 247.
88. [87] M.B. Halpern, "Recent Developments in the Virasoro Master Equation", in the proceedings of the Stony Brook conference, Strings and Symmetries 1991, World Scientific, 1992.
89. [88] M.B. Halpern, "Recent Progress in Irrational Conformal Field Theory", in the Proceedings of the Berkeley Conference, Strings '93 (World Scientific, Singapore, 1995).
90. [89] M.B. Halpern, "Irrational Conformal Field Theory on the Sphere and the Torus" Berkeley preprint, UCB-PTH-94/33, hep-th/9411209. To appear in the proceedings of the XIth International Congress of Mathematical Physics, Paris, July 1994.
91. [90] M.B. Halpern, unpublished (1994).
92. [91] M.B. Halpern and E. Kiritsis, Mod. Phys. Lett. A 4 (1989) 1373; Erratum ibid. A 4 (1989) 1797.
93. [92] M.B. Halpern, E. Kiritsis and N.A. Obers, unpublished (1991).
94. [93] M.B. Halpern, E. Kiritsis and N.A. Obers, "The Lie h-Invariant Conformal Field Theories and the Lie h-Invariant Graphs", in the proceedings of the RIMS Research Project 1991, Infinite Analysis; Int. J. Mod. Phys. A 7, [Suppl. 1A] (1992) 339.
95. [93] M.B. Halpern, E. Kiritsis and N.A. Obers, "The Lie h-Invariant Conformal Field Theories and the Lie h-Invariant Graphs", in the proceedings of the RIMS Research Project 1991, Infinite Analysis; Int. J. Mod. Phys. A 7, [Suppl. 1A] (1992) 339.
96. [94] M.B. Halpern, E. Kiritsis, N.A. Obers, M. Porrati and J.P. Yamron, Int. J. Mod. Phys. A 5 (1990) 2275.
97. [95] M.B. Halpern and N.A. Obers, Int. J. Mod. Phys. A 6 (1991) 1835.
98. [96] M.B. Halpern and N.A. Obers, Nucl. Phys. B 345 (1990) 607.
99. [97] M.B. Halpern and N.A. Obers, Comm. Math. Phys. 138 (1991) 63.
100. [98] M.B. Halpern and N.A. Obers, Ann. of Phys. 212 (1991) 28.
101. [99] M.B. Halpern and N.A. Obers, Int. J. Mod. Phys. A 7 (1992) 7263.
102. [100] M.B. Halpern and N.A. Obers, Int. J. Mod. Phys. A 7 (1992) 3065.
103. [101] M.B. Halpern and N.A. Obers, J. Math. Phys. 32 (1991) 3231.
104. [102] M.B. Halpern and N.A. Obers, J. Math. Phys. 33 (1992) 3274.
105. [103] M.B. Halpern and N.A. Obers, Int. J. Mod. Phys. A 9 (1994) 265.
106. [104] M.B. Halpern and N.A. Obers, Int. J. Mod. Phys. A 9 (1994) 419.
107. [105] M.B. Halpern and N.A. Obers, J. Math. Phys. 36 (1995) 1080.
108. [106] M.B. Halpern and N. Sochen, Int. J. Mod. Phys. A 10 (1995) 1181.
109. [107] M.B. Halpern and C.B. Thorn, Phys. Rev. D 4 (1971) 3084.
110. [108] M.B. Halpern and J.P. Yamron, Nucl. Phys. B 332 (1990) 411.
111. [109] M.B. Halpern and J.P. Yamron, Nucl. Phys. B 351 (1991) 333.
112. [110] F. Harary, "Graph Theory", London, Addison-Wesley, 1972.
113. [111] F. Harary and E.M. Palmer, "Graphical Enumeration", New York, Academic Press, 1973.
114. [112] S. Hwang and H. Rhedin, Nucl. Phys. B 406 (1993) 165.
115. [113] S. Hwang and H. Rhedin, "General Branching Functions of Affine Lie Algebras", Göteborg preprint, ITP 94-8, hep-th/9408087.
116. [114] V.F.R. Jones, "Subfactors and Knots", American Math. Soc. CBMS Lecture series No. 80 (1991).
117. [115] V.G. Kač, Funct. Anal. App. 1 (1967) 328.
118. [116] V.G. Kač, Adv. Math. 26 (1977) 8.
119. [117] V.G. Kač, "Infinite dimensional Lie algebras", Cambridge Univ. Press, 1985.
120. [118] V.G. Kač and D.H. Peterson, Adv. Math. 53 (1984) 125.
121. [119] V.G. Kač and M. Wakimoto, Adv. Math. 70 (1988) 156.
122. [120] D. Karabali, Q-H. Park and H.J. Schnitzer, Phys. Lett. B 205 (1988) 267.
123. [121] D. Karabali, Q-H. Park and H.J. Schnitzer, Nucl. Phys. B 323 (1989) 572.
124. [122] D. Karabali, Q-H. Park, H.J. Schnitzer and Z. Yang, Phys. Lett. B 216 (1989) 307.
125. [123] D. Karabali and H.J. Schnitzer, Nucl. Phys. B 329 (1990) 649.
126. [124] Y. Kazama and H. Suzuki, Mod. Phys. Lett. A 4 (1989) 235.
127. [125] Y. Kazama and H. Suzuki, Nucl. Phys. B 321 (1989) 232.
128. [126] Y. Kazama and H. Suzuki, Phys. Lett. B 216 (1989) 112.
129. [127] A.A. Kehagias, "All WZW Models in D ≤ 5", Athens Technical Univ. preprint, NTUA-45-94A, hep-th/9406136.
130. [128] A.A. Kehagias and P.A.A. Meessen, Phys. Lett. B 331 (1994) 77.
131. [129] V.G. Knizhnik and A.B. Zamolodchikov, Nucl. Phys. B 247 (1984) 83.
132. [130] E. Kiritsis, Mod. Phys. Lett. A 4 (1989) 437.
133. [131] E. Kiritsis and C. Kounnas, Phys. Lett. B 320 (1994) 264.
134. [132] E. Kiritsis, C. Kounnas and D. Lüst, Phys. Lett. B 331 (1994) 321.
135. [133] O. Klein, J. Phys. Radium 9 (1938) 1.
136. [134] M.Yu. Lashkevich, "Conformal Blocks of Coset Construction: Zero Ghost Number", Landau Inst. preprint, LANDAU-92-TMP-1, hep-th/9301094.
137. [135] J. Lepowsky and R.L. Wilson, Comm. Math. Phys. 62 (1978) 43.
138. [136] S. Mandelstam, Phys. Rev. D 7 (1973) 3777.
139. [137] S. Mandelstam, Phys. Rev. D 11 (1975) 3026.
140. [138] J. Milnor, "Morse Theory", Princeton University Press, 1963.
141. [139] S. Mizoguchi, Int. J. Mod. Phys. A 6 (1991) 133.
142. [140] N. Mohammedi, Phys. Lett. B 260 (1991) 317.
143. [141] N. Mohammedi, Phys. Lett. B 325 (1994) 371.
144. [142] N. Mohammedi, Phys. Lett. B 337 (1994) 279.
145. [143] R.V. Moody, Bull. Am. Math. Soc. 73 (1967) 217.
146. [144] A.Yu Morozov, A.M. Perelomov, A.A. Rosly, M.A. Shifman and A.V. Turbiner, Int. J. Mod. Phys. A 5 (1990) 803.
147. [145] A.Yu Morozov, M.A. Shifman and A.V. Turbiner, Int. J. Mod. Phys. A 5 (1990) 2953.
148. [146] C.R. Nappi and E. Witten, Phys. Rev. Lett. 71 (1993) 3751.
149. [147] A. Neveu and J.H. Schwarz, Nucl. Phys. B 31 (1971) 86.
150. [148] S.P. Novikov, Usp. Math. Nauk. 37 (1982) 3.
151. [149] D.I. Olive, E. Rabinovici and A. Schwimmer, Phys. Lett. B 321 (1994) 361.
152. [150] J. Patera and H. Zassenhaus, J. Math. Phys. 29 (1988) 665.
153. [151] A.M. Polyakov, Int. J. Mod. Phys. A 5 (1990) 833.
154. [152] S. Popa, Acta Math. 172 No. 2 (1994) 163.
155. [153] C. Pope, L. Romans and X. Shen, Nucl. Phys. B 339 (1990) 191.
156. [154] E. Ragoucy and P. Sorba, Phys. Lett. B 256 (1991) 30.
157. [155] E. Raiten, Int. J. Mod. Phys. A 6 (1991) 1713.
158. [156] P. Ramond, Phys. Rev. D 3 (1971) 2415.
159. [157] L.J. Romans, Nucl. Phys. B 352 (1991) 829.
160. [158] S. Schrans, "Extensions of Conformal Invariance in Two-Dimensional Quantum Field Theory", Ph.D. thesis, Leuven, 1991, unpublished.
161. [159] S. Schrans, Class. Quant. Grav. 10 (1993) 173.
162. [160] S. Schrans and W. Troost, Nucl. Phys. B 345 (1990) 584.
163. [161] G. Segal, Comm. Math. Phys. 80 (1981) 301.
164. [162] G. Segal, unpublished.
165. [163] J.J. Seidel, "Graphs and their spectra", in "Combinatorics and Graph Theory", Banach Center Public 25 (1989) 147.
166. [164] K. Sfetsos, Phys. Lett. B 324 (1994) 335.
167. [165] K. Sfetsos, Int. J. Mod. Phys. A 9 (1994) 4759.
168. [166] K. Sfetsos, Phys. Rev. D 50 (1994) 2784.
169. [167] W. Siegel, Nucl. Phys. B 109 (1976) 244.
170. [168] O.A. Soloviev, Mod. Phys. Lett. A 8 (1993) 301.
171. [169] O.A. Soloviev, Mod. Phys. Lett. A 8 (1993) 3071.
172. [170] O.A. Soloviev, Mod. Phys. Lett. A 9 (1994) 483.
173. [171] O.A. Soloviev, "Conformal Non-Abelian Thirring Models", Queen Mary preprint, QMW-93-19, hep-th/9307163.
174. [172] O.A. Soloviev, "Solutions of the Virasoro Master Equations as Conformal Points of Perturbed WZNW Model", Queen Mary preprint, QMW-94-24, hep-th/9408034.
175. [173] O.A. Soloviev, "Conformal Invariance of Interacting WZNW Models", Queen Mary preprint, QMW-94-26, hep-th/9408112.
176. [174] C. Sommerfeld, Phys. Rev. 176 (1968) 2019.
177. [175] H. Sugawara, Phys. Rev. 170 (1968) 1659.
178. [176] W. Taylor, "Coadjoint Orbits and Conformal Field Theory", Ph.D. thesis, Berkeley, 1993, UCB-PTH-93/26, hep-th/9310040.
179. [177] A.A. Tseytlin, Nucl. Phys. B 418 (1994) 173.
180. [178] M.A. Virasoro, Phys. Rev. D 1 (1970) 2933.
181. [179] J.H. Weis, as quoted in R.C. Brower and C.B. Thorn, Nucl. Phys. B 31 (1971) 163.
182. [180] P. Windey, Comm. Math. Phys. 105 (1986) 511.
183. [181] E. Witten, Comm. Math. Phys. 92 (1984) 455.
184. [182] E. Witten, "The Central Charge in Three Dimensions", in Memorial Volume for V. Knizhnik, ed. L. Brink et al., World Scientific, 1990.
185. [183] A.B. Zamolodchikov, Theor. Math. Phys. 65 (1985) 1205.
186. [184] A.B. Zamolodchikov, Sov. J. Nucl. Phys. 44 (1986) 529.
187. [185] A.B. Zamolodchikov, JETP Lett. 43 (1986) 730.