Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
SpringerLink
Log in

The quantum deformed mirror TBA I

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We derive the ground state thermodynamic Bethe ansatz equations for the quantum deformation of the AdS5 × S5 mirror model, taking the deformation parameter to be a root of unity. By virtue of the deformation, the resulting equations show an interesting structure between a finite number of Y-functions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113 ] [hep-th/9711200] [INSPIRE].

    MathSciNet  ADS  MATH  Google Scholar 

  2. N. Beisert et al., Review of AdS/CFT integrability: an overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  3. G. Arutyunov and S. Frolov, Foundations of the AdS 5 × S 5 superstring. Part I, J. Phys. A 42 (2009) 254003 [arXiv:0901.4937] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  4. G. Arutyunov and S. Frolov, Thermodynamic Bethe Ansatz for the AdS 5 × S 5 mirror model, JHEP 05 (2009) 068 [arXiv:0903.0141] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  5. 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] [INSPIRE].

    MathSciNet  Google Scholar 

  6. 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] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. A. Zamolodchikov, Thermodynamic Bethe ansatz in relativistic models. Scaling three state potts and Lee-Yang models, Nucl. Phys. B 342 (1990) 695 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. G. Arutyunov and S. Frolov, On string S-matrix, bound states and TBA, JHEP 12 (2007) 024 [arXiv:0710.1568] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. N. Beisert, The SU(2|2) dynamic S-matrix, Adv. Theor. Math. Phys. 12 (2008) 945 [hep-th/0511082] [INSPIRE].

    MathSciNet  Google Scholar 

  10. N. Beisert and P. Koroteev, Quantum deformations of the one-dimensional Hubbard model, J. Phys. A 41 (2008) 255204 [arXiv:0802.0777] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  11. N. Beisert, W. Galleas and T. Matsumoto, A quantum affine algebra for the deformed Hubbard chain, J. Phys. A 45 (2012) 365206 [arXiv:1102.5700] [INSPIRE].

    MathSciNet  Google Scholar 

  12. B. Hoare, T.J. Hollowood and J.L. Miramontes, q-deformation of the AdS 5 × S 5 superstring S-matrix and its relativistic limit, JHEP 03 (2012) 015 [arXiv:1112.4485] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  13. B. Hoare, T.J. Hollowood and J.L. Miramontes, Bound states of the q-deformed AdS 5 × S 5 superstring S-matrix, arXiv:1206.0010 [INSPIRE].

  14. N. Beisert, The classical trigonometric r-matrix for the quantum-deformed Hubbard chain, J. Phys. A 44 (2011) 265202 [arXiv:1002.1097] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  15. B. Hoare and A. Tseytlin, Towards the quantum S-matrix of the Pohlmeyer reduced version of AdS 5 × S 5 superstring theory, Nucl. Phys. B 851 (2011) 161 [arXiv:1104.2423] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  16. B. Hoare, T.J. Hollowood and J.L. Miramontes, A relativistic relative of the magnon S-matrix, JHEP 11 (2011) 048 [arXiv:1107.0628] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  17. M. Takahashi and M. Suzuki, A reply to the comments of Johnson et al. on the thermodynamics of the Heisenberg-Ising ring for |Δ| < 1, Phys. Lett. A 41 (1972) 81.

    ADS  Google Scholar 

  18. M. Takahashi, Thermodynamics of one-dimensional solvable models, Cambridge University Press, Cambridge U.K. (1999).

    Book  Google Scholar 

  19. A. Kuniba, T. Nakanishi and J. Suzuki, T-systems and Y-systems in integrable systems, J. Phys. A 44 (2011) 103001 [arXiv:1010.1344] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  20. Z. Bajnok, Review of AdS/CFT Integrability, Chapter III.6: Thermodynamic Bethe Ansatz, Lett. Math. Phys. 99 (2012) 299 [arXiv:1012.3995] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. G. Arutyunov and S. Frolov, String hypothesis for the AdS 5 × S 5 mirror, JHEP 03 (2009) 152 [arXiv:0901.1417] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. 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] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  23. A. Cavaglia, D. Fioravanti and R. Tateo, Extended Y-system for the AdS 5 /CF T 4 correspondence, Nucl. Phys. B 843 (2011) 302 [arXiv:1005.3016] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. A. Cavaglia, D. Fioravanti, M. Mattelliano and R. Tateo, On the AdS 5 /CF T 4 TBA and its analytic properties, arXiv:1103.0499 [INSPIRE].

  25. J. Balog and A. Hegedus, AdS 5 × S 5 mirror TBA equations from Y-system and discontinuity relations, JHEP 08 (2011) 095 [arXiv:1104.4054] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. J. Balog and A. Hegedus, Quasi-local formulation of the mirror TBA, JHEP 05 (2012) 039 [arXiv:1106.2100] [INSPIRE].

    Article  ADS  Google Scholar 

  27. A. Klumper and P. Pearce, Conformal weights of RSOS lattice models and their fusion hierarchies, Physica A 183 (1992) 304 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  28. A. Klumper and P. Pearce, New results for exactly solvable critical RSOS models and vertex models in two dimensions, Physica A 194 (1993) 397.

    MathSciNet  ADS  Google Scholar 

  29. P. Dorey and R. Tateo, Excited states by analytic continuation of TBA equations, Nucl. Phys. B 482 (1996) 639 [hep-th/9607167] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  30. 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] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. G. Arutyunov and S. Frolov, Comments on the mirror TBA, JHEP 05 (2011) 082 [arXiv:1103.2708] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  32. G. Arutyunov, S. Frolov and R. Suzuki, Exploring the mirror TBA, JHEP 05 (2010) 031 [arXiv:0911.2224] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. J. Balog and A. Hegedus, The Bajnok-Janik formula and wrapping corrections, JHEP 09 (2010) 107 [arXiv:1003.4303] [INSPIRE].

    Article  ADS  Google Scholar 

  34. A. Sfondrini and S.J. van Tongeren, Lifting asymptotic degeneracies with the Mirror TBA, JHEP 09 (2011) 050 [arXiv:1106.3909] [INSPIRE].

    Article  ADS  Google Scholar 

  35. G. Arutyunov, S. Frolov and S.J. van Tongeren, Bound states in the mirror TBA, JHEP 02 (2012) 014 [arXiv:1111.0564] [INSPIRE].

    Article  ADS  Google Scholar 

  36. G. Arutyunov, S. Frolov and A. Sfondrini, Exceptional operators in N = 4 super Yang-Mills, JHEP 09 (2012) 006 [arXiv:1205.6660] [INSPIRE].

    Article  ADS  Google Scholar 

  37. G. Arutyunov, S. Frolov and R. Suzuki, Five-loop Konishi from the mirror TBA, JHEP 04 (2010) 069 [arXiv:1002.1711] [INSPIRE].

    Article  ADS  Google Scholar 

  38. J. Balog and A. Hegedus, 5-loop Konishi from linearized TBA and the XXX magnet, JHEP 06 (2010) 080 [arXiv:1002.4142] [INSPIRE].

    Article  ADS  Google Scholar 

  39. 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] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. 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] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  41. T. Lukowski, A. Rej and V. Velizhanin, Five-loop anomalous dimension of twist-two operators, Nucl. Phys. B 831 (2010) 105 [arXiv:0912.1624] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  42. R.A. Janik, Review of AdS/CFT integrability. Chapter III.5: Lúscher Corrections, Lett. Math. Phys. 99 (2012) 277 [arXiv:1012.3994] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  43. 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] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  44. 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] [INSPIRE].

    Article  ADS  Google Scholar 

  45. 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][INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  46. 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] [INSPIRE].

    Article  ADS  Google Scholar 

  47. N. Drukker, Integrable Wilson loops, arXiv:1203.1617 [INSPIRE].

  48. N. Gromov, V. Kazakov, S. Leurent and D. Volin, Solving the AdS/CFT Y-system, JHEP 07 (2012) 023 [arXiv:1110.0562] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  49. J. Balog and A. Hegedus, Hybrid-NLIE for the AdS/CFT spectral problem, JHEP 08 (2012) 022 [arXiv:1202.3244] [INSPIRE].

    Article  ADS  Google Scholar 

  50. R. Suzuki, Hybrid NLIE for the mirror AdS 5 × S 5, J. Phys. A 44 (2011) 235401 [arXiv:1101.5165] [INSPIRE].

    ADS  Google Scholar 

  51. R. Suzuki, Contour deformation trick in hybrid NLIE, JHEP 07 (2012) 152 [arXiv:1202.3947] [INSPIRE].

    Article  ADS  Google Scholar 

  52. N. Gromov and A. Sever, Analytic Solution of Bremsstrahlung TBA, arXiv:1207.5489 [INSPIRE].

  53. N. Gromov and F. Levkovich-Maslyuk, Y-system and β-deformed N = 4 super-Yang-Mills, J. Phys. A 44 (2011) 015402 [arXiv:1006.5438] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  54. G. Arutyunov, M. de Leeuw and S.J. van Tongeren, Twisting the mirror TBA, JHEP 02 (2011) 025 [arXiv:1009.4118] [INSPIRE].

    ADS  Google Scholar 

  55. M. de Leeuw and S.J. van Tongeren, Orbifolded Konishi from the mirror TBA, J. Phys. A 44 (2011) 325404 [arXiv:1103.5853] [INSPIRE].

    Google Scholar 

  56. M. Beccaria and G. Macorini, Y-system for Z S orbifolds of N = 4 SYM, JHEP 06 (2011) 004 [Erratum ibid. 1201 (2012) 112] [arXiv:1104.0883] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  57. C. Ahn, Z. Bajnok, D. Bombardelli and R.I. Nepomechie, TBA, NLO Lüscher correction and double wrapping in twisted AdS/CFT, JHEP 12 (2011) 059 [arXiv:1108.4914] [INSPIRE].

    Article  ADS  Google Scholar 

  58. M. de Leeuw and S.J. van Tongeren, The spectral problem for strings on twisted AdS 5 × S 5, Nucl. Phys. B 860 (2012) 339 [arXiv:1201.1451] [INSPIRE].

    Article  ADS  Google Scholar 

  59. G. Arutyunov, M. de Leeuw and Stijn J. van Tongeren, The quantum deformed mirror TBA II, to appear.

  60. A. Mostafazadeh, Pseudo-Hermiticity versus PT symmetry: The Structure responsible for the reality of the spectrum of a nonHermitian Hamiltonian, math-ph/0107001 [INSPIRE].

  61. 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] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  62. H. Saleur and B. Wehefritz-Kaufmann, Thermodynamics of the complex SU(3) Toda theory, Phys. Lett. B 481 (2000) 419 [hep-th/0003217] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  63. 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].

    MathSciNet  ADS  Google Scholar 

  64. L. Faddeev, How algebraic Bethe ansatz works for integrable model, hep-th/9605187 [INSPIRE].

  65. G. Arutyunov and S. Frolov, Simplified TBA equations of the AdS 5 × S 5 mirror model, JHEP 11 (2009) 019 [arXiv:0907.2647] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  66. M. Gaudin, Thermodynamics of the Heisenberg-Ising ring for Δ ≥ 1, Phys. Rev. Lett. 26 (1971)1301.

    Article  ADS  Google Scholar 

  67. G. Arutyunov, S. Frolov and M. Staudacher, Bethe ansatz for quantum strings, JHEP 10 (2004) 016 [hep-th/0406256] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  68. N. Beisert, B. Eden and M. Staudacher, Transcendentality and Crossing, J. Stat. Mech. 0701 (2007) P01021 [hep-th/0610251] [INSPIRE].

    Article  Google Scholar 

  69. R.A. Janik, The AdS 5 × S 5 superstring worldsheet S-matrix and crossing symmetry, Phys. Rev. D 73 (2006) 086006 [hep-th/0603038] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  70. G. Arutyunov and S. Frolov, The Dressing Factor and Crossing Equations, J. Phys. A 42 (2009) 425401 [arXiv:0904.4575] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  71. 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] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  72. S. Frolov and R. Suzuki, Temperature quantization from the TBA equations, Phys. Lett. B 679 (2009) 60 [arXiv:0906.0499] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  73. S. Frolov and E. Quinn, Hubbard-Shastry lattice models, J. Phys. A 45 (2012) 095004 [arXiv:1111.5304] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  74. 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.

    MathSciNet  ADS  Google Scholar 

  75. M. Fowler and X. Zotos, Quantum sine-Gordon thermodynamics: the Bethe ansatz method, Phys. Rev. B 24 (1981) 2634 [INSPIRE].

    ADS  Google Scholar 

  76. M. de Leeuw, T. Matsumoto and V. Regelskis, The bound state Scmatrix of the deformed Hubbard chain, JHEP 04 (2012) 021 [arXiv:1109.1410] [INSPIRE].

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Leuvenlaan 4, 3584 CE, Utrecht, The Netherlands

    Gleb Arutyunov & Stijn J. van Tongeren

  2. ETH Zürich, Institut für Theoretische Physik, Wolfgang-Pauli-Str. 27, CH-8093, Zurich, Switzerland

    Marius de Leeuw

Authors
  1. Gleb Arutyunov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marius de Leeuw
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Stijn J. van Tongeren
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stijn J. van Tongeren.

Additional information

ArXiv ePrint: 1208.3478

Correspondent fellow at Steklov Mathematical Institute, Moscow. (Gleb Arutyunov)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Arutyunov, G., de Leeuw, M. & van Tongeren, S.J. The quantum deformed mirror TBA I. J. High Energ. Phys. 2012, 90 (2012). https://doi.org/10.1007/JHEP10(2012)090

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP10(2012)090

Keywords

Search

Navigation