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S-matrix for strings on η-deformed AdS5 × S5

  • Gleb Arutyunov
  • Riccardo Borsato
  • Sergey Frolov
Open Access
Article

Abstract

We determine the bosonic part of the superstring sigma model Lagrangian on η-deformed AdS5 × S5, and use it to compute the perturbative world-sheet scattering matrix of bosonic particles of the model. We then compare it with the large string tension limit of the q-deformed S-matrix and find exact agreement.

Keywords

AdS-CFT Correspondence Bosonic Strings Exact S-Matrix Integrable Field Theories 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [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].ADSMATHMathSciNetGoogle Scholar
  2. [2]
    S. Kachru and E. Silverstein, 4 − D conformal theories and strings on orbifolds, Phys. Rev. Lett. 80 (1998) 4855 [hep-th/9802183] [INSPIRE].ADSCrossRefMATHMathSciNetGoogle Scholar
  3. [3]
    A.E. Lawrence, N. Nekrasov and C. Vafa, On conformal field theories in four-dimensions, Nucl. Phys. B 533 (1998) 199 [hep-th/9803015] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  4. [4]
    O. Lunin and J.M. Maldacena, Deforming field theories with U(1) × U(1) global symmetry and their gravity duals, JHEP 05 (2005) 033 [hep-th/0502086] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  5. [5]
    S. Frolov, Lax pair for strings in Lunin-Maldacena background, JHEP 05 (2005) 069 [hep-th/0503201] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    N. Beisert and P. Koroteev, Quantum Deformations of the One-Dimensional Hubbard Model, J. Phys. A 41 (2008) 255204 [arXiv:0802.0777] [INSPIRE].ADSMathSciNetGoogle Scholar
  7. [7]
    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].MathSciNetGoogle Scholar
  8. [8]
    B. Hoare, T.J. Hollowood and J.L. Miramontes, q-Deformation of the AdS 5 xS 5 Superstring S-matrix and its Relativistic Limit, JHEP 03 (2012) 015 [arXiv:1112.4485] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  9. [9]
    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] [INSPIRE].CrossRefGoogle Scholar
  10. [10]
    S.J. van Tongeren, Integrability of the AdS 5 × S 5 superstring and its deformations, arXiv:1310.4854 [INSPIRE].
  11. [11]
    G. Arutyunov, M. de Leeuw and S.J. van Tongeren, The quantum deformed mirror TBA I, JHEP 10 (2012) 090 [arXiv:1208.3478] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    G. Arutyunov, M. de Leeuw and S.J. van Tongeren, The quantum deformed mirror TBA II, JHEP 02 (2013) 012 [arXiv:1210.8185] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    N. Beisert, The classical trigonometric r-matrix for the quantum-deformed Hubbard chain, J. Phys. A 44 (2011) 265202 [arXiv:1002.1097] [INSPIRE].ADSMathSciNetGoogle Scholar
  14. [14]
    B. Hoare, T.J. Hollowood and J.L. Miramontes, Restoring unitarity in the q-deformed world-sheet S-matrix, JHEP 10 (2013) 050 [arXiv:1303.1447] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    F. Delduc, M. Magro and B. Vicedo, An integrable deformation of the AdS 5 × S 5 superstring action, Phys. Rev. Lett. 112 (2014) 051601 [arXiv:1309.5850] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    I. Cherednik, Relativistically invariant quasiclassical limits of integrable two-dimensional quantum models, Theor. Math. Phys. 47 (1981) 422 [INSPIRE].CrossRefMathSciNetGoogle Scholar
  17. [17]
    C. Klimčík, On integrability of the Yang-Baxter σ-model, J. Math. Phys. 50 (2009) 043508 [arXiv:0802.3518] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  18. [18]
    C. Klimčík, Yang-Baxter σ-models and dS/AdS T duality, JHEP 12 (2002) 051 [hep-th/0210095] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    F. Delduc, M. Magro and B. Vicedo, On classical q-deformations of integrable σ-models, JHEP 11 (2013) 192 [arXiv:1308.3581] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  20. [20]
    I. Kawaguchi, T. Matsumoto and K. Yoshida, The classical origin of quantum affine algebra in squashed σ-models, JHEP 04 (2012) 115 [arXiv:1201.3058] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  21. [21]
    I. Kawaguchi, T. Matsumoto and K. Yoshida, On the classical equivalence of monodromy matrices in squashed σ-model, JHEP 06 (2012) 082 [arXiv:1203.3400] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  22. [22]
    T. Klose, T. McLoughlin, R. Roiban and K. Zarembo, Worldsheet scattering in AdS 5 × S 5, JHEP 03 (2007) 094 [hep-th/0611169] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  23. [23]
    G. Arutyunov, R. Borsato and S. Frolov, work in progress.Google Scholar
  24. [24]
    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].ADSMathSciNetGoogle Scholar
  25. [25]
    G. Arutyunov, S. Frolov and M. Zamaklar, The Zamolodchikov-Faddeev algebra for AdS 5 × S 5 superstring, JHEP 04 (2007) 002 [hep-th/0612229] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  26. [26]
    G. Arutyunov, S. Frolov and M. Staudacher, Bethe ansatz for quantum strings, JHEP 10 (2004) 016 [hep-th/0406256] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  27. [27]
    D.M. Hofman and J.M. Maldacena, Giant Magnons, J. Phys. A 39 (2006) 13095 [hep-th/0604135] [INSPIRE].MathSciNetGoogle Scholar
  28. [28]
    G. Arutyunov, S. Frolov and M. Zamaklar, Finite-size Effects from Giant Magnons, Nucl. Phys. B 778 (2007) 1 [hep-th/0606126] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  29. [29]
    S. Gubser, I. Klebanov and A.M. Polyakov, A semiclassical limit of the gauge/string correspondence, Nucl. Phys. B 636 (2002) 99 [hep-th/0204051] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  30. [30]
    S. Frolov and A.A. Tseytlin, Semiclassical quantization of rotating superstring in AdS 5 × S 5, JHEP 06 (2002) 007 [hep-th/0204226] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  31. [31]
    G. Arutyunov, S. Frolov, J. Russo and A.A. Tseytlin, Spinning strings in AdS 5 × S 5 and integrable systems, Nucl. Phys. B 671 (2003) 3 [hep-th/0307191] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  32. [32]
    G. Arutyunov, M. de Leeuw and S.J. van Tongeren, On the exact spectrum and mirror duality of the (AdS 5 × S 5)η superstring, arXiv:1403.6104 [INSPIRE].
  33. [33]
    M. Jimbo, H. Konno and T. Miwa, Massless XXZ model and degeneration of the elliptic algebra \( {A_{q,p }}\left( {\widehat{{s{l_2}}}} \right) \) , hep-th/9610079 [INSPIRE].
  34. [34]
    S. Britton and S. Frolov, Free field representation and form factors of the chiral Gross-Neveu model, JHEP 11 (2013) 076 [arXiv:1305.6252] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Gleb Arutyunov
    • 1
  • Riccardo Borsato
    • 1
  • Sergey Frolov
    • 2
    • 3
  1. 1.Institute for Theoretical Physics and Spinoza InstituteUtrecht UniversityUtrechtThe Netherlands
  2. 2.Institut für Mathematik und Institut für Physik, Humboldt-Universität zu BerlinBerlinGermany
  3. 3.Hamilton Mathematics Institute and School of MathematicsTrinity CollegeDublin 2Ireland

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