Integrable sigma models and perturbed coset models

Journal of High Energy Physics

Volumn 5, Issue 5, 2001, Pages

  Fendley, Paul ^a  

^a University of Virginia   (United States)

Author keywords

Bethe ansatz; Exact s matrix; Integrable field theories; Sigma models

Indexed keywords

EID: 33744774729     PISSN: 10298479     EISSN: None     Source Type: Journal    
DOI: 10.1088/1126-6708/2001/05/050     Document Type: Article

References (108)

1. D.H. Friedan, Nonlinear models in two + e dimensions, Ann. Phys. (NY) 163 (1985) 318.
2. F.D. M. Haldane, Continuum dynamics of the Id Heisenberg antiferromagnetic identification with the O(3) nonlinear sigma model, Phys. Lett. A 93 (1983) 464; Nonlinear field theory of large spin heisenberg antiferromagnets. Semiclassically quantized solitons of the one-dimensional easy axis neel state, Phys. Rev. Lett. 50 (1983) 1153; F.D.M. Haldane, Q Physics' and quantum spin chains, J. Appl. Phys., 57 (1985) 3359; I. Affleck, The quantum hall effect, sigma models at 9 = vr and quantum spin chains, Nucl. Phys. B 257 (1985) 397.
3. A.M.M. Pruisken, On localization in the theory of the quantized hall effect: a twodimensional realization of the theta vacuum, Nucl. Phys. B 235 (1984) 277.
4. A.B. Zamolodchikov and A.B. Zamolodchikov, Massless factorized scattering and sigma models with topological terms, Nucl. Phys. B 379 (1992) 602.
5. P. Fendley, Integrable sigma models with 9 = vr, cond-mat/0008372.
6. For a review see I. Affleck, Quantum field theory and critical phenomena, in Fields, strings and critical phenomena, North-Holland 1988.
7. P. Fendley, Critical points in two-dimensional replica sigma models, cond-mat/0006360.
8. A.B. Zamolodchikov, 'Irreversibility' of the flux of the renormalization group in a 2 -D field theory, Sov. Phys. JETP Lett. 43 (1986) 730.
9. R.M. Konik and P. Fendley, to appear soon.
10. V.A. Fateev, E. Onofri and A.B. Zamolodchikov, The sausage model (integrable deformations o/O(3) sigma model), Nucl. Phys. B 406 (1993) 521.
11. A. Zamolodchikov and A. Zamolodchikov, Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field models, Annals Phys. 120 (1979) 253.
12. P. Hasenfratz, M. Maggiore and F. Niedermayer, The exact mass gap of the O(3) and O(4) nonlinear sigma models in D = 2, Phys. Lett. B 245 (1990) 522.
13. M. Karowski and H.J. Thun, Complete s matrix of the O(2n) Gross-Neveu model, Nucl. Phys. B 190 (1981) 61.
14. E. Ogievetsky, P. Wiegmann and N. Reshetikhin, The principal chiral field in twodimensions on classical Lie algebras: the bethe ansatz solution and factorized theory of scattering, Nucl. Phys. B 280 (1987) 45.
15. N.J. MacKay, New factorized s matrices associated with SO(N), Nucl. Phys. B 356 (1991) 729.
16. P.P. Kulish, N.Y. Reshetikhin and E.K. Sklyanin, Yang-Baxter equation and representation theory: I, Lett. Math. Phys. 5 (1981) 393.
17. R. Cahn, Semi-Simple Lie Algebras and their Representations, Benjamin-Cummings, 1984, available for free at http://www-physics.lbl.gov/rncahn/book.html
18. C.N. Yang and C.P. Yang, Thermodynamics of one-dimensional system of bosons with repulsive delta function interaction, J. Math. Phys. 10 (1969) 1115.
19. A.B. Zamolodchikov, Thermodynamic bethe ansatz in relativistic models. Scaling three state potts and Lee-Yang models, Nucl. Phys. B 342 (1990) 695.
20. H.W.J. Bloete, J.L. Cardy and M.P. Nightingale, Conformai invariance, the central charge and universal finite size amplitudes at criticality, Phys. Rev. Lett. 56 (1986) 742.
21. A. Kirillov and N.Yu. Reshetikhin, Exact solution of the integrable XXZ Heisenberg model with arbitrary spin, 2. Thermodynamics of the system, J. Phys. A20 (1987) 1587.
22. V.V. Bazhanov and N.Yu. Reshetikhin, Critical RSOS models and conformai field theory, Int. J. Mod. Phys. A 4 (1989) 115.
23. V. Bazhanov and N. Reshetikhin, Restricted solid on solid models connected with simply based algebras and conformai field theory, J. Phys. A23 (1990) 1477
24. V.V. Bazhanov and N.Yu. Reshetikhin, Scattering Amplitudes In Off Critical Models And RSOS Integrable Models, Prog. Theor. Phys. Suppl., 102 (1990) 301.
25. P.B. Wiegmann, Exact solution of the O(3) nonlinear sigma model, Phys. Lett. B 152 (1985) 209.
26. A.M. Tsvelik, (1 + 1) -dimensional sigma model at finite temperatures, Sov. Phys. JETP 66 (1987) 221.
27. V.A. Fateev and A.B. Zamolodchikov, Integrable perturbations of Z(JV) parafermion models and O(3) sigma model, Phys. Lett. B 271 (1991) 91.
28. H. Bethe, On the theory of metals. 1. Eigenvalues and eigen]'unctions for the linear atomic chain, Z. Phys. 71 (1931) 205.
29. M. Fowler, X. Zotos, Bethe-ansatz quantum sine-Gordon thermodynamics: the specific heat, Phys. Rev. B 25 (1982) 5806.
30. P. Fendley and H. Saleur, Massless integrable quantum field theories and massless scattering in (1 + 1)-dimensions, hep-th/9310058.
31. N. Andrei and J.H. Lowenstein, Diagonalization of the chiral invariant Gross-Neveu hamiltonian, Phys. Rev. Lett. 43 (1979) 1698; Derivation of the chiral Gross-Neveu spectrum for arbitrary SU(N) symmetry, Phys. Lett. B 90 (1980) 106.
32. B. Berg and P. Weisz, Exact s matrix of the chiral invariant SU(N) thirring model, Nucl. Phys. B 146 (1978) 205;
33. R. Koberle, V. Kurak and J.A. Swieca, Scattering theory and I/N expansion in the chiral Gross-Neveu model, Phys. Rev. D 20 (1979) 897.
34. A. Kuniba, T. Nakanishi and J. Suzuki, Functional relations in solvable lattice models. 1: functional relations and representation theory, Int. J. Mod. Phys. A 9 (1994) 5215 [hep-th/9309137]; Functional relations in solvable lattice model 2: applications, Int. J. Mod. Phys. A 9 (1994) 5267 [hep-th/9310060].
35. T.J. Hollowood, From A(m-l) trigonometric S matrices to the thermodynamic Bethe ansatz, Phys. Lett. B 320 (1994) 43 [hep-th/9308147].
36. E. Quattrini, F. Ravanini and R. Tateo, Integrable QFT in two-dimensions encoded on products of Dynkin diagrams, hep-th/9311116.
37. D.J. Gross and A. Neveu, Dynamical symmetry breaking in asymptotically free field theories, Phys. Rev. D 10 (1974) 3235.
38. 2 model in two- dimensions, Nucl. Phys. B 142 (1978) 285.
39. P. Fendley, Sigma models as perturbed conformai field theories, Phys. Rev. Lett. 83 (1999) 4468 [hep-th/9906036].
40. E. Witten, Nonabelian bosonization in two dimensions, Comm. Math. Phys. 92 (1984) 455.
41. V.G. Knizhnik and A.B. Zamolodchikov, Current algebra and Wess-Zumino model in two dimensions, Nud. Phys. B 247 (1984) 83.
42. P. Goddard, A. Kent and D. Olive, Unitary representations of the Virasoro and supervirasoro algebras, Comm. Math. Phys. 103 (1986) 105.
43. J. Zinn-Justin, Quantum field theory and critical phenomena, Oxford 1989.
44. C. Ahn, D. Bernard and A. LeClair, Fractional super-symmetries in perturbed coset CFTS and integrable soliton theory, Nucl. Phys. B 346 (1990) 409.
45. A.W. W. Ludwig and J.L. Cardy, Perturbative evaluation of the conformai anomaly at new critical points with applications to random systems, Nucl. Phys. B 285 (1987) 687.
46. D. Altschuler, Quantum equivalence of coset space models, Nucl. Phys. B 313 (1989) 293.
47. R. Koberle and J.A. Swieca, Factorizable Z(N) models, Phys. Lett. B 86 (1979) 209.
48. T.R. Klassen and E. Melzer, Purely elastic scattering theories and their ultraviolet limits, Nucl. Phys. B 338 (1990) 485.
49. V.A. Fateev, The sigma model (dual) representation for a two-parameter family of integrable quantum field theories, Nucl. Phys. B 473 (1996) 509.
50. I. Vaysburd, Critical rsos models in external fields, Nucl. Phys. B 446 (1995) 387 [hep-th/9503070]; Integrable perturbations of W(N) and WZW models, Phys. Lett. B 335 (1994) 161 [hep-th/9402061].
51. V. Pasquier and H. Saleur, Common structures between finite systems and conformai field theories through quantum groups, Nucl. Phys. B 330 (1990) 523.
52. A.B. Zamolodchikov, unpublished preprint, 1989.
53. G. Andrews, R. Baxter and P. Forrester, Eight vertex SOS model and generalized Rogers-Ramanujan type identities, J. Stat. Phys. 35 (1984) 193.
54. H.J. de Vega and V.A. Fateev, Factorizable S matrices for perturbed W invariant theories, Int. J. Mod. Phys. A 6 (1991) 3221.
55. M. Jimbo, T. Miwa and M. Okado, Solvable lattice models related to the vector representation of classical simple Lie algebras, Comm. Math. Phys. 116 (1988) 507.
56. E. Date, M. Jimbo, T. Miwa and M. Okado, Fusion of the eight vertex SOS model, Lett. Math. Phys. 12 (1986) 209.
57. E. Abdalla, M.C. B. Abdalla and M. Forger, Exact s matrices for anomaly free nonlinear sigma models on symmetric spaces, Nucl. Phys. B 297 (1988) 374.
58. E. Witten, Instantons, the quark model and the l/N expansion, Nucl. Phys. B 149 (1979) 285.
59. A. Altland and M. Zirnbauer, Novel symmetry classes in mesoscopic normalsuperconducting hybrid structures, Phys. Rev. B 55 (1998) 1142, [cond-mat/9602137]; M. Zirnbauer, Riemannian symmetric super-spaces and their origin in random matrix theory, J. Math. Phys. 37 (1996) 4986 [math.ph/9808012].
60. M. Luscher, Quantum nonlocal charges and absence of particle production in the twodimensional nonlinear sigma model, Nucl. Phys. B 135 (1978) 1.
61. D. Bernard, Hidden yangians in 2 -d massive current algebras, Comm. Math. Phys. 137 (1991) 191.
62. J.M. Evans and A.J. Mountain, Commuting charges and symmetric spaces, Phys. Lett. B 483 (2000) 290 [hep-th/0003264].
63. DO collaboration, Inclusive JJL and b quark production cross-sections inpp collisions at √s = 1.8 TeV, Phys. Rev. Lett. 74 (1995) 3548.
64. DO collaboration, The bb production cross-section and angular correlations in pp collisions at √s = 1.8 TeV Phys. Lett. B 487 (2000) 264 [hep-ex/9905024].
65. CDF collaboration, Measurement of the bottom quark production cross-section using semileptonic decay electrons in pp collisions at √s = 1.8 TeV, Phys. Rev. Lett. 71 (1993) 500; Measurement of bottom quark production in 1.8 TeV pp collisions using semileptonic decay muons, Phys. Rev. Lett. 71 (1993) 2396;
66. c and b-quark production inpp collisions at √s = 1.8 TeV, Phys. Rev. Lett. 71 (1993) 2537;
67. Measurement of the B meson differential cross-section, da/dpT, in pp collisions at √s = 1.8 TeV, Phys. Rev. Lett. 75 (1995) 1451 [hep-ex/9503013].
68. DO collaboration, Small angle muon and bottom quark production in pp collisions at √s = 1.8 TeV, Phys. Rev. Lett. 84 (2000) 5478 [hep-ex/9907029].
69. P. Nason, S. Dawson and R.K. Ellis, The total cross-section for the production of heavy quarks in hadronic collisions, Nucl. Phys. B 303 (1988) 607.
70. M.L. Mangano, P. Nason and G. Ridolfi, Heavy quark correlations in hadron collisions at next-to-leading order, Nucl. Phys. B 373 (1992) 295.
71. W. Beenakker, W.L. van Neerven, R. Meng, G.A. Schuler and J. Smith, QCD corrections to heavy quark production in hadron-hadron collisions, Nucl. Phys. B 351 (1991) 507.
72. HI collaboration, Measurement of open beauty production at HERA, Phys. Lett. B 467 (1999) 156 [hep-ex/9909029].
73. ZEUS collaboration, Measurement of open beauty production in photoproduction at HERA, Eur. Phys. J. C 18 (2001) 625 [hep-ex/0011081].
74. L3 collaboration, Measurements of the cross sections for open charm and beauty production in 77 collisions at √s = 189 GeV - 202 GeV, Phys. Lett. B 503 (2001) 10 [hep-ex/0011070].
75. OPAL collaboration, Charm and bottom production in two-photon collisions with OPAL, hep-ex/0010060.
76. S. Frixione and M.L. Mangano, Heavy-quark jets in hadronic collisions, Nucl. Phys. B 483 (1997) 321 [hep-ph/9605270].
77. DO collaboration, Cross section for B jet production inpp collisions at √s = 1.8 TeV, Phys. Rev. Lett. 85 (2000) 5068 [hep-ex/0008021].
78. R. Bonciani, S. Catani, M.L. Mangano and P. Nason, NLL resummation of the heavyquark hadroproduction cross-section, Nucl. Phys. B 529 (1998) 424 [hep-ph/9801375].
79. R.K. Ellis and D.A. Ross, The coupling of the QCD pomeron in various semihard processes, Nucl. Phys. B 345 (1990) 79.
80. S. Catani, M. Ciafaloni and F. Hautmann, Gluon contributions to small x heavy flavor production, Phys. Lett. B 242 (1990) 97.
81. J.C. Collins and R.K. Ellis, Heavy quark production in very high-energy hadron collisions, Nucl. Phys. B 360 (1991) 3.
82. S. Catani, M. Ciafaloni and F. Hautmann, High-energy factorization and small x heavy flavor production, Nucl. Phys. B 366 (1991) 135.
83. S. Catani, M. Ciafaloni and F. Hautmann, Production of heavy flavors at high-energies, CERN-TH-6398-92, presented at the Workshop on Physics at HERA, Hamburg, Germany, Oct 29-30, 1991.
84. G. Camici and M. Ciafaloni, Non-abelian qq contributions to small-x anomalous dimensions, Phys. Lett. B 386 (1996) 341 [hep-ph/9606427].
85. G. Camici and M. Ciafaloni, k-factorization and small-x anomalous dimensions, Nucl. Phys. B 496 (1997) 305 [hep-ph/9701303].
86. P. Hagler, R. Kirschner, A. Schafer, L. Szymanowski and O. Teryaev, Heavy quark hadroproduction as a test of the effective BFKL qq vertex, Phys. Rev. D 62 (2000) 071502 [hep-ph/0002077].
87. M.G. Ryskin, Y.M. Shabelski and A.G. Shuvaev, Heavy quark production in hadron collisions, hep-ph/0011111.
88. R.D. Ball and S. Forte, Double asymptotic scaling at HERA, Phys. Lett. B 335 (1994) 77 [hep-ph/9405320]; A direct test of perturbative QCD at small x, Phys. Lett. B 336 (1994) 77 [hep-ph/9406385].
89. R.D. Ball and S. Forte, Summation of leading logarithms at small x, Phys. Lett. B 351 (1995) 313 [hep-ph/9501231].
90. R.K. Ellis, F. Hautmann and B.R. Webber, QCD scaling violation at small x, Phys. Lett. B 348 (1995) 582 [hep-ph/9501307].
91. S. Forte and R.D. Ball, Double scaling violations, hep-ph/9607291.
92. 2 data, Nucl. Phys. B 508 (1997) 731 [hep-ph/9702282].
93. J. Blumlein and A. Vogt, The evolution of unpolarized singlet structure functions at small x, Phys. Rev. D 58 (1998) 014020 [hep-ph/9712546].
94. V.S. Fadin and L.N. Lipatov, Bfklpomeron in the next-to-leading approximation, Phys. Lett. B 429 (1998) 127 [hep-ph/9802290].
95. D.A. Ross, The effect of higher order corrections to the BFKL equation on the perturbative pomeron, Phys. Lett. B 431 (1998) 161 [hep-ph/9804332].
96. R.D. Ball and S. Forte, Corrections at small x, hep-ph/9805315.
97. Y.V. Kovchegov and A.H. Mueller, Running coupling effects in BFKL evolution, Phys. Lett. B 439 (1998) 428 [hep-ph/9805208].
98. N. Armesto, J. Bartels and M.A. Braun, On the 2nd order corrections to the hard pomeron and the running coupling, Phys. Lett. B 442 (1998) 459 [hep-ph/9808340].
99. G.P. Salani, A resummation of large sub-leading corrections at small x, J. High Energy Phys. 07 (1998) 019 [hep-ph/9806482].
100. R.D. Ball and S. Forte, The small x behaviour of Altarelli-Parisi splitting functions, Phys. Lett. B 465 (1999) 271 [hep-ph/9906222].
101. M. Ciafaloni, D. Colferai and G.P. Salam, Renormalization group improved small-x equation, Phys. Rev. D 60 (1999) 114036 [hep-ph/9905566].
102. G. Altarelli, R.D. Ball and S. Forte, Resummation of singlet parton evolution at small x, Nucl. Phys. B 575 (2000) 313 [hep-ph/9911273].
103. G. Altarelli, R.D. Ball and S. Forte, Small-x resummation and hera structure function data, Nucl. Phys. B 599 (2001) 383 [hep-ph/0011270].
104. R.K. Ellis and P. Nason, QCD radiative corrections to the photoproduction of heavy quarks, Nucl. Phys. B 312 (1989) 551.
105. S. Catani, Comment on quarks and gluons at small x and the SDIS factorization scheme, Z. Physik C 70 (1996) 263 [hep-ph/9506357]; Quarks and gluons at small x and scaling violation of F2, hep-ph/9506348.
106. R.D. Ball and S. Forte, Momentum conservation at small x, Phys. Lett. B 359 (1995) 362 [hep-ph/9507321].
107. S. Catani and F. Hautmann, High-energy factorization and small x deep inelastic scattering beyond leading order, Nucl. Phys. B 427 (1994) 475 [hep-ph/9405388].
108. A.D. Rujula, S.L. Glashow, H.D. Politzer, S.B. Treiman, F. Wilczek and A. Zee, Possible nonregge behavior of electroproduction structure functions, Phys. Rev. D 10 (1974) 1649.