Skip to main content
Log in

Twist operators in N = 4 betadeformed theory

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

Abstract

In this paper we derive both the leading order finite size corrections for twist-2 and twist-3 operators and the next-to-leading order finite-size correction for twist-2 operators in beta-deformed SYM theory. The obtained results respect the principle of maximum transcendentality as well as reciprocity. We also find that both wrapping corrections go to zero in the large spin limit. Moreover, for twist-2 operators we studied the pole structure and compared it against leading BFKL predictions.

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

Access this article

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

Instant access to the full article PDF.

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] [SPIRES].

    MathSciNet  ADS  MATH  Google Scholar 

  2. N. Beisert and M. Staudacher, Long-range PSU(2, 24) Bethe ansaetze for gauge theory and strings, Nucl. Phys. B 727 (2005) 1 [hep-th/0504190] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  3. M. Lüscher, Volume dependence of the energy spectrum in massive quantum field theories. 1. Stable particle states, Commun. Math. Phys. 104 (1986) 177 [SPIRES].

    Article  ADS  MATH  Google Scholar 

  4. R.A. Janik and T. Lukowski, Wrapping interactions at strong coupling — The giant magnon, Phys. Rev. D 76 (2007) 126008 [arXiv:0708.2208] [SPIRES].

    ADS  Google Scholar 

  5. 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] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  6. F. Fiamberti, A. Santambrogio, C. Sieg and D. Zanon, Anomalous dimension with wrapping at four loops in N = 4 SYM, Nucl. Phys. B 805 (2008) 231 [arXiv:0806.2095] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  7. V.N. 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] [SPIRES].

    Article  ADS  Google Scholar 

  8. Z. Bajnok, R.A. Janik and T. Lukowski, Four loop twist two, BFKL, wrapping and strings, Nucl. Phys. B 816 (2009) 376 [arXiv:0811.4448] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  9. 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] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  11. M. Beccaria, V. Forini, T. Lukowski and S. Zieme, Twist-three at five loops, Bethe ansatz and wrapping, JHEP 03 (2009) 129 [arXiv:0901.4864] [SPIRES].

    Article  ADS  Google Scholar 

  12. V.N. Velizhanin, Six-loop anomalous dimension of twist-three operators in N =4 SYM, JHEP 11 (2010) 129 [arXiv:1003.4717] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  14. 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] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  15. 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] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. 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] [SPIRES].

    MathSciNet  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  23. C. Ahn, Z. Bajnok, D. Bombardelli and R.I. Nepomechie, Finite-size effect for four-loop Konishi of the beta-deformed N =4 SYM, Phys. Lett. B 693 (2010) 380 [arXiv:1006.2209] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  24. C. Ahn, Z. Bajnok, D. Bombardelli and R.I. Nepomechie, Twisted Bethe equations from a twisted S-matrix, JHEP 02 (2011) 027 [arXiv:1010.3229] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  25. F. Fiamberti, A. Santambrogio, C. Sieg and D. Zanon, Finite-size effects in the superconformal beta-deformed N =4 SYM, JHEP 08 (2008) 057 [arXiv:0806.2103] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  26. F. Fiamberti, A. Santambrogio, C. Sieg and D. Zanon, Single impurity operators at critical wrapping order in the beta-deformed N =4 SYM, JHEP 08 (2009) 034 [arXiv:0811.4594] [SPIRES].

    Article  ADS  Google Scholar 

  27. M. Beccaria, F. Levkovich-Maslyuk and G. Macorini, On wrapping corrections to GKP-like operators, JHEP 03 (2011) 001 [arXiv:1012.2054] [SPIRES].

    Article  ADS  Google Scholar 

  28. L.N. Lipatov, Reggeization of the vector meson and the vacuum singularity in nonabelian gauge theories, Sov. J. Nucl. Phys. 23 (1976) 338 [SPIRES].

    Google Scholar 

  29. E.A. Kuraev, L.N. Lipatov and V.S. Fadin, The Pomeranchuk singularity in nonabelian gauge theories, Sov. Phys. JETP 45 (1977) 199 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  30. I.I. Balitsky and L.N. Lipatov, The Pomeranchuk singularity in quantum chromodynamics, Sov. J. Nucl. Phys. 28 (1978) 822 [SPIRES].

    Google Scholar 

  31. Y.L. Dokshitzer, G. Marchesini and G.P. Salam, Revisiting parton evolution and the large-x limit, Phys. Lett. B 634 (2006) 504 [hep-ph/0511302] [SPIRES].

    ADS  Google Scholar 

  32. Y.L. Dokshitzer and G. Marchesini, N =4 SUSY Yang-Mills: Three loops made simple(r), Phys. Lett. B 646 (2007) 189 [hep-th/0612248] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  33. B. Basso and G.P. Korchemsky, Anomalous dimensions of high-spin operators beyond the leading order, Nucl. Phys. B 775 (2007) 1 [hep-th/0612247] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  34. M. Beccaria and V. Forini, Four loop reciprocity of twist two operators in N =4 SYM, JHEP 03 (2009) 111 [arXiv:0901.1256] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  35. V. Forini and M. Beccaria, QCD-like properties for anomalous dimensions in N =4 SYM, Theor. Math. Phys. 159 (2009) 712 [arXiv:0810.0101] [SPIRES].

    Article  MathSciNet  MATH  Google Scholar 

  36. M. Beccaria, Y.L. Dokshitzer and G. Marchesini, Twist 3 of the sl(2) sector of N =4 SYM and reciprocity respecting evolution, Phys. Lett. B 652 (2007) 194 [arXiv:0705.2639] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  37. M. Beccaria, Three loop anomalous dimensions of twist-3 gauge operators in N =4 SYM, JHEP 09 (2007) 023 [arXiv:0707.1574] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  38. M. Beccaria, Anomalous dimensions at twist-3 in the sl(2) sector of N =4 SYM, JHEP 06 (2007) 044 [arXiv:0704.3570] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  39. M. Beccaria, V. Forini, A. Tirziu and A.A. Tseytlin, Structure of large spin expansion of anomalous dimensions at strong coupling, Nucl. Phys. B 812 (2009) 144 [arXiv:0809.5234] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  40. M. Beccaria, G.V. Dunne, V. Forini, M. Pawellek and A.A. Tseytlin, Exact computation of one-loop correction to energy of spinning folded string in AdS 5 × S 5, J. Phys. A 43 (2010) 165402 [arXiv:1001.4018] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  41. G.P. Korchemsky, Asymptotics of the Altarelli-Parisi-Lipatov evolution kernels of parton distributions, Mod. Phys. Lett. A4 (1989) 1257 [SPIRES].

    ADS  Google Scholar 

  42. G.P. Korchemsky and G. Marchesini, Structure function for large x and renormalization of Wilson loop, Nucl. Phys. B 406 (1993) 225 [hep-ph/9210281] [SPIRES].

    Article  ADS  Google Scholar 

  43. Z. Bern, M. Czakon, L.J . Dixon, D.A. Kosower and V.A. Smirnov, The four-loop planar amplitude and cusp anomalous dimension in maximally supersymmetric Yang-Mills theory, Phys. Rev. D 75 (2007) 085010 [hep-th/0610248] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  44. B. Basso, G.P. Korchemsky and J. Kotanski, Cusp anomalous dimension in maximally supersymmetric Yang-Mills theory at strong coupling, Phys. Rev. Lett. 100 (2008) 091601 [arXiv:0708.3933] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  45. N. Beisert, B. Eden and M. Staudacher, Transcendentality and crossing, J. Stat. Mech. (2007) P01021 [hep-th/0610251] [SPIRES].

  46. S.E. Derkachov, G.P. Korchemsky and A.N. Manashov, Separation of variables for the quantum SL(2,R) spin chain, JHEP 07 (2003) 047 [hep-th/0210216] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  47. B. Eden and M. Staudacher, Integrability and transcendentality, J. Stat. Mech. (2006) P11014 [hep-th/0603157] [SPIRES].

  48. A.V. Kotikov, L.N. Lipatov, A. Rej, M. Staudacher and V.N. Velizhanin, Dressing and wrapping, J. Stat. Mech. (2007) P10003 [arXiv:0704.3586] [SPIRES].

  49. J. Gunnesson, Wrapping in maximally supersymmetric and marginally deformed N =4 Yang-Mills, JHEP 04 (2009) 130 [arXiv:0902.1427] [SPIRES].

    Article  ADS  Google Scholar 

  50. G. Arutyunov, M. de Leeuw, R. Suzuki and A. Torrielli, Bound state transfer matrix for AdS 5 × S 5 superstring, JHEP 10 (2009) 025 [arXiv:0906.4783] [SPIRES].

    Article  ADS  Google Scholar 

  51. G. Arutyunov and S. Frolov, The dressing factor and crossing equations, J. Phys. A 42 (2009) 425401 [arXiv:0904.4575] [SPIRES].

    MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tomasz Lukowski.

Additional information

ArXiv ePrint:1012.3725

Rights and permissions

Reprints and permissions

About this article

Cite this article

de Leeuw, M., Lukowski, T. Twist operators in N = 4 betadeformed theory. J. High Energ. Phys. 2011, 84 (2011). https://doi.org/10.1007/JHEP04(2011)084

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP04(2011)084

Keywords

Navigation