The quantum deformed mirror TBA I

Journal of High Energy Physics

Volumn 2012, Issue 10, 2012, Pages

  Arutyunov, Gleb ^a,c   De Leeuw, Marius ^b   Van Tongeren, Stijn J ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

^b ETH ZURICH   (Switzerland)

^c STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

AdS CFT Correspondence; Bethe Ansatz; Integrable Field Theories; Quantum Groups

Indexed keywords

EID: 84868270166     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP10(2012)090     Document Type: Article

References (77)

1. J.M. Maldacena, the large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231
2. [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200].
3. N. Beisert et al., Review of AdS/CFT integrability: an overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982].
4. G. Arutyunov and S. Frolov, Foundations of the AdS5 - S5 superstring. Part I, J. Phys. A 42 (2009) 254003 [arXiv:0901.4937].
5. G. Arutyunov and S. Frolov, Thermodynamic Bethe Ansatz for the AdS5 - S5 mirror model, JHEP 05 (2009) 068 [arXiv:0903.0141].
6. D. Bombardelli, D. Fioravanti and R. Tateo, Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal, J. Phys. A 42 (2009) 375401 [arXiv:0902.3930].
7. N. Gromov, V. Kazakov, A. Kozak and P. Vieira, Exact spectrum of anomalous dimensions of planar N = 4 superSYMmetric Yang-Mills theory: TBA and excited states, Lett. Math. Phys. 91 (2010) 265 [arXiv:0902.4458].
8. A. Zamolodchikov, Thermodynamic Bethe ansatz in relativistic models. Scaling three state potts and Lee-Yang models, Nucl. Phys. B 342 (1990) 695.
9. G. Arutyunov and S. Frolov, On string S-matrix, bound states and TBA, JHEP 12 (2007) 024 [arXiv:0710.1568].
10. N. Beisert, the SU(2j2) dynamic S-matrix, Adv. Theor. Math. Phys. 12 (2008) 945 [hep-th/0511082].
11. N. Beisert and P. Koroteev, Quantum deformations of the one-dimensional Hubbard model, J. Phys. A 41 (2008) 255204 [arXiv:0802.0777].
12. N. Beisert, W. Galleas and T. Matsumoto, A quantum afine algebra for the deformed Hubbard chain, J. Phys. A 45 (2012) 365206 [arXiv:1102.5700].
13. B. Hoare, T.J. Hollowood and J.L. Miramontes, q-deformation of the AdS5 - S5 superstring S-matrix and its relativistic limit, JHEP 03 (2012) 015 [arXiv:1112.4485].
14. B. Hoare, T.J. Hollowood and J.L. Miramontes, Bound states of the q-deformed AdS5 - S5 superstring S-matrix, arXiv:1206.0010.
15. N. Beisert, the classical trigonometric r-matrix for the quantum-deformed Hubbard chain, J. Phys. A 44 (2011) 265202 [arXiv:1002.1097].
16. B. Hoare and A. Tseytlin, Towards the quantum S-matrix of the Pohlmeyer reduced version of AdS5 - S5 superstring theory, Nucl. Phys. B 851 (2011) 161 [arXiv:1104.2423].
17. B. Hoare, T.J. Hollowood and J.L. Miramontes, A relativistic relative of the magnon S-matrix, JHEP 11 (2011) 048 [arXiv:1107.0628].
18. M. Takahashi and M. Suzuki, A reply to the comments of Johnson et al. on the thermodynamics of the Heisenberg-Ising ring for J-J < 1, Phys. Lett. A 41 (1972) 81.
19. M. Takahashi, Thermodynamics of one-dimensional solvable models, Cambridge University Press, Cambridge U.K. (1999).
20. A. Kuniba, T. Nakanishi and J. Suzuki, T-systems and Y-systems in integrable systems, J. Phys. A 44 (2011) 103001 [arXiv:1010.1344].
21. Z. Bajnok, Review of AdS/CFT Integrability, Chapter III.6: Thermodynamic Bethe Ansatz, Lett. Math. Phys. 99 (2012) 299 [arXiv:1012.3995].
22. G. Arutyunov and S. Frolov, String hypothesis for the AdS5 - S5 mirror, JHEP 03 (2009) 152 [arXiv:0901.1417].
23. N. Gromov, V. Kazakov and P. Vieira, Exact spectrum of anomalous dimensions of planar N = 4 superSYMmetric Yang-Mills theory, Phys. Rev. Lett. 103 (2009) 131601 [arXiv:0901.3753].
24. A. Cavaglia, D. Fioravanti and R. Tateo, Extended Y-system for the AdS5=CFT4 correspondence, Nucl. Phys. B 843 (2011) 302 [arXiv:1005.3016].
25. A. Cavaglia, D. Fioravanti, M. Mattelliano and R. Tateo, On the AdS5=CFT4 TBA and its analytic properties, arXiv:1103.0499.
26. J. Balog and A. Hegedus, AdS5 - S5 mirror TBA equations from Y-system and discontinuity relations, JHEP 08 (2011) 095 [arXiv:1104.4054].
27. J. Balog and A. Hegedus, Quasi-local formulation of the mirror TBA, JHEP 05 (2012) 039 [arXiv:1106.2100].
28. A. Klumper and P. Pearce, Conformal weights of RSOS lattice models and their fusion hierarchies, Physica A 183 (1992) 304.
29. A. Klumper and P. Pearce, New results for exactly solvable critical RSOS models and vertex models in two dimensions, Physica A 194 (1993) 397.
30. P. Dorey and R. Tateo, Excited states by analytic continuation of TBA equations, Nucl. Phys. B 482 (1996) 639 [hep-th/9607167].
31. V.V. Bazhanov, S.L. Lukyanov and A.B. Zamolodchikov, Integrable quantum field theories in finite volume: excited state energies, Nucl. Phys. B 489 (1997) 487 [hep-th/9607099].
32. G. Arutyunov and S. Frolov, Comments on the mirror TBA, JHEP 05 (2011) 082 [arXiv:1103.2708].
33. G. Arutyunov, S. Frolov and R. Suzuki, Exploring the mirror TBA, JHEP 05 (2010) 031 [arXiv:0911.2224].
34. J. Balog and A. Hegedus, the Bajnok-Janik formula and wrapping corrections, JHEP 09 (2010) 107 [arXiv:1003.4303].
35. A. Sfondrini and S.J. van Tongeren, Lifting aSYMptotic degeneracies with the Mirror TBA, JHEP 09 (2011) 050 [arXiv:1106.3909].
36. G. Arutyunov, S. Frolov and S.J. van Tongeren, Bound states in the mirror TBA, JHEP 02 (2012) 014 [arXiv:1111.0564].
37. G. Arutyunov, S. Frolov and A. Sfondrini, Exceptional OPERAtors in N = 4 super Yang-Mills, JHEP 09 (2012) 006 [arXiv:1205.6660].
38. G. Arutyunov, S. Frolov and R. Suzuki, Five-loop Konishi from the mirror TBA, JHEP 04 (2010) 069 [arXiv:1002.1711].
39. J. Balog and A. Hegedus, 5-loop Konishi from linearized TBA and the XXX magnet, JHEP 06 (2010) 080 [arXiv:1002.4142].
40. Z. Bajnok and R.A. Janik, Four-loop perturbative Konishi from strings and finite size effects for multiparticle states, Nucl. Phys. B 807 (2009) 625 [arXiv:0807.0399].
41. Z. Bajnok, A. Hegedus, R.A. Janik and T. Lukowski, Five loop Konishi from AdS/CFT, Nucl. Phys. B 827 (2010) 426 [arXiv:0906.4062].
42. T. Lukowski, A. Rej and V. Velizhanin, Five-loop anomalous dimension of twist-two OPERAtors, Nucl. Phys. B 831 (2010) 105 [arXiv:0912.1624].
43. R.A. Janik, Review of AdS/CFT integrability. Chapter III.5: Lúscher Corrections, Lett. Math. Phys. 99 (2012) 277 [arXiv:1012.3994].
44. F. Fiamberti, A. Santambrogio, C. Sieg and D. Zanon, Wrapping at four loops in N = 4 SYM, Phys. Lett. B 666 (2008) 100 [arXiv:0712.3522].
45. V. Velizhanin, the four-loop anomalous dimension of the Konishi OPERAtor in N = 4 superSYMmetric Yang-Mills theory, JETP Lett. 89 (2009) 6 [arXiv:0808.3832].
46. B. Eden, P. Heslop, G.P. Korchemsky, V.A. Smirnov and E. Sokatchev, Five-loop Konishi in N = 4 SYM, Nucl. Phys. B 862 (2012) 123 [arXiv:1202.5733].
47. D. Correa, J. Maldacena and A. Sever, the quark anti-quark potential and the cusp anomalous dimension from a TBA equation, JHEP 08 (2012) 134 [arXiv:1203.1913].
48. N. Drukker, Integrable Wilson loops, arXiv:1203.1617.
49. N. Gromov, V. Kazakov, S. Leurent and D. Volin, Solving the AdS/CFT Y-system, JHEP 07 (2012) 023 [arXiv:1110.0562].
50. J. Balog and A. Hegedus, Hybrid-NLIE for the AdS/CFT spectral problem, JHEP 08 (2012) 022 [arXiv:1202.3244].
51. R. Suzuki, Hybrid NLIE for the mirror AdS5 - S5, J. Phys. A 44 (2011) 235401 [arXiv:1101.5165].
52. R. Suzuki, Contour deformation trick in hybrid NLIE, JHEP 07 (2012) 152 [arXiv:1202.3947].
53. N. Gromov and A. Sever, Analytic Solution of Bremsstrahlung TBA, arXiv:1207.5489.
54. N. Gromov and F. Levkovich-Maslyuk, Y-system and -deformed N = 4 super-Yang-Mills, J. Phys. A 44 (2011) 015402 [arXiv:1006.5438].
55. G. Arutyunov, M. de Leeuw and S.J. van Tongeren, Twisting the mirror TBA, JHEP 02 (2011) 025 [arXiv:1009.4118].
56. M. de Leeuw and S.J. van Tongeren, Orbifolded Konishi from the mirror TBA, J. Phys. A 44 (2011) 325404 [arXiv:1103.5853].
57. M. Beccaria and G. Macorini, Y-system for ZS orbifolds of N = 4 SYM, JHEP 06 (2011) 004
58. C. Ahn, Z. Bajnok, D. Bombardelli and R.I. Nepomechie, TBA, NLO Luscher correction and double wrapping in twisted AdS/CFT, JHEP 12 (2011) 059 [arXiv:1108.4914].
59. M. de Leeuw and S.J. van Tongeren, the spectral problem for strings on twisted AdS5 - S5, Nucl. Phys. B 860 (2012) 339 [arXiv:1201.1451].
60. G. Arutyunov, M. de Leeuw and Stijn J. van Tongeren, the quantum deformed mirror TBA II, to appear.
61. A. Mostafazadeh, Pseudo-Hermiticity versus PT SYMmetry: the Structure responsible for the reality of the spectrum of a nonHermitian Hamiltonian, math-ph/0107001.
62. A. Mostafazadeh, PseudoHermiticity versus PT SYMmetry 2. A complete characterization of nonHermitian Hamiltonians with a real spectrum, J. Math. Phys. 43 (2002) 2814 [math-ph/0110016].
63. H. Saleur and B. Wehefritz-Kaufmann, Thermodynamics of the complex SU(3) Toda theory, Phys. Lett. B 481 (2000) 419 [hep-th/0003217].
64. F.C. Alcaraz and R.Z. Bariev, Interpolation between Hubbard and superSYMmetric t-J models: two-parameter integrable models of correlated electrons, J. Phys. A 32 (1999) L483 [cond-mat/9908265].
65. L. Faddeev, How algebraic Bethe ansatz works for integrable model, hep-th/9605187.
66. G. Arutyunov and S. Frolov, Simplified TBA equations of the AdS5 - S5 mirror model, JHEP 11 (2009) 019 [arXiv:0907.2647].
67. M. Gaudin, Thermodynamics of the Heisenberg-Ising ring for 1, Phys. Rev. Lett. 26 (1971) 1301.
68. G. Arutyunov, S. Frolov and M. Staudacher, Bethe ansatz for quantum strings, JHEP 10 (2004) 016 [hep-th/0406256].
69. N. Beisert, B. Eden and M. Staudacher, Transcendentality and Crossing, J. Stat. Mech. 0701 (2007) P01021 [hep-th/0610251].
70. R.A. Janik, the AdS5 - S5 superstring worldsheet S-matrix and crossing SYMmetry, Phys. Rev. D 73 (2006) 086006 [hep-th/0603038].
71. G. Arutyunov and S. Frolov, the Dressing Factor and Crossing Equations, J. Phys. A 42 (2009) 425401 [arXiv:0904.4575].
72. N. Dorey, D.M. Hofman and J.M. Maldacena, On the singularities of the magnon S-matrix, Phys. Rev. D 76 (2007) 025011 [hep-th/0703104].
73. S. Frolov and R. Suzuki, Temperature quantization from the TBA equations, Phys. Lett. B 679 (2009) 60 [arXiv:0906.0499].
74. S. Frolov and E. Quinn, Hubbard-Shastry lattice models, J. Phys. A 45 (2012) 095004 [arXiv:1111.5304].
75. M. Hida, Rigorous derivation of the distribution of the eigenstates of the quantum Heisenberg-Ising chain with XY-like anisotropy, Phys. Lett. A 84 (1981) 338.
76. M. Fowler and X. Zotos, Quantum sine-Gordon thermodynamics: the Bethe ansatz method, Phys. Rev. B 24 (1981) 2634.
77. M. de Leeuw, T. Matsumoto and V. Regelskis, the bound state S-matrix of the deformed Hubbard chain, JHEP 04 (2012) 021 [arXiv:1109.1410].