Skip to main content
SpringerLink
Log in

Exact Spectrum of Anomalous Dimensions of Planar N = 4 Supersymmetric Yang–Mills Theory: TBA and excited states

  • Published:
Letters in Mathematical Physics Aims and scope Submit manuscript

Abstract

Using the thermodynamic Bethe ansatz method we derive an infinite set of integral non-linear equations for the spectrum of states/operators in AdS/CFT. The Y-system conjectured in Gromov et al. (Integrability for the Full Spectrum of Planar AdS/CFT. arXiv:0901.3753 [hep-th]) for the spectrum of all operators in planar N = 4 SYM theory follows from these equations. In particular, we present the integral TBA type equations for the spectrum of all operators within the sl(2) sector. We prove that all the kernels and free terms entering these TBA equations are real and have nice fusion properties in the relevant mirror kinematics. We find the analog of DHM formula for the dressing kernel in the mirror kinematics.

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

Access this article

Log in via an institution

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. Gromov, N., Kazakov, V., Vieira, P.: Integrability for the Full Spectrum of Planar AdS/CFT. arXiv:0901.3753 [hep-th]

  2. Kazakov V., Sorin A., Zabrodin A.: Supersymmetric Bethe ansatz and Baxter equations from discrete Hirota dynamics. Nucl. Phys. B 790, 345 (2008) arXiv:hep-th/0703147

    Article  MATH  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  4. Staudacher M.: The factorized S-matrix of CFT/AdS. JHEP 0505, 054 (2005) arXiv:hep-th/0412188

    Article  MathSciNet  ADS  Google Scholar 

  5. Beisert N., Staudacher M.: Long-range PSU(2, 2|4) Bethe ansaetze for gauge theory and strings. Nucl. Phys. B 727, 1–62 (2005) hep-th/0504190

    Article  MATH  MathSciNet  ADS  Google Scholar 

  6. Beisert N.: The SU(2|2) dynamic S-matrix. Adv. Theor. Math. Phys. 12, 945 (2008) arXiv:hep-th/0511082

    MathSciNet  Google Scholar 

  7. Beisert N., Eden B., Staudacher M.: Transcendentality and crossing. J. Stat. Mech. 0701, P021 (2007) hep-th/0610251

    Google Scholar 

  8. Bajnok Z., Janik R.A.: Four-loop perturbative Konishi from strings and finite size effects for multiparticle states. Nucl. Phys. B 807, 625 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  9. Bajnok, Z., Janik, R.A., Lukowski, T.: Four loop twist two, BFKL, wrapping and strings. arXiv:0811.4448 [hep-th]

  10. Fiamberti F., Santambrogio A., Sieg C., Zanon D.: Anomalous dimension with wrapping at four loops in N = 4 SYM. Nucl. Phys. B 805, 231 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  11. Velizhanin, V.N.: Leading transcedentality contributions to the four-loop universal anomalous dimension in N = 4 SYM. arXiv:0811.0607 [hep-th]

  12. Zamolodchikov Al.B.: On the thermodynamic Bethe ansatz equations for reflectionless ADE scattering theories. Phys. Lett. B 253, 391 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  13. Gromov, N., Kazakov, V., Vieira, P.: Finite Volume Spectrum of 2D Field Theories from Hirota Dynamics. arXiv:0812.5091 [hep-th]

  14. Arutyunov, G., Frolov, S.: Foundations of the AdS 5 x S 5 Superstring. Part I. arXiv:0901.4937 [hep-th]

  15. Arutyunov G., Frolov S.: On String S-matrix, Bound States and TBA. JHEP 0712, 024 (2007) arXiv:0710.1568 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  16. Dorey N.: Magnon bound states and the AdS/CFT correspondence. J. Phys. A 39, 13119 (2006) arXiv:hep-th/0604175

    Article  MATH  MathSciNet  Google Scholar 

  17. Dorey P., Tateo R.: Excited states by analytic continuation of TBA equations. Nucl. Phys. B 482, 639 (1996) arXiv:hep-th/9607167

    Article  MATH  MathSciNet  ADS  Google Scholar 

  18. Bazhanov V.V., Lukyanov S.L., Zamolodchikov A.B.: Quantum field theories in finite volume: Excited state energies. Nucl. Phys. B 489, 487 (1997) arXiv:hep-th/9607099

    Article  MATH  MathSciNet  ADS  Google Scholar 

  19. Fioravanti D., Mariottini A., Quattrini E., Ravanini F.: Phys. Lett. B 390, 243 (1997) arXiv:hep-th/9608091

    Article  MathSciNet  ADS  Google Scholar 

  20. Teschner J.: On the spectrum of the Sinh-Gordon model in finite volume. Nucl. Phys. B 799, 403 (2008) arXiv:hep-th/0702214

    Article  MATH  MathSciNet  ADS  Google Scholar 

  21. Ambjorn J., Janik R.A., Kristjansen C.: Wrapping interactions and a new source of corrections to the spin-chain/string duality. Nucl. Phys. B 736, 288–301 (2006) hep-th/0510171

    Article  MathSciNet  ADS  Google Scholar 

  22. Dorey N., Hofman D.M., Maldacena J.M.: Phys. Rev. D 76, 025011 (2007) arXiv: hep-th/0703104

    Article  MathSciNet  Google Scholar 

  23. Takahashi : Thermodynamics of One-Dimensional Solvable Models. Cambridge University Press, Cambridge (1999)

    Book  Google Scholar 

  24. Essler F.H.L., Frahm H., Göhmann F., Klümper A., Korepin V.: The One-Dimensional Hubbard Model. Cambridge University Press. Cambridge University Press, Cambridge (2005)

    Book  MATH  Google Scholar 

  25. Arutyunov, G., Frolov, S.: String hypothesis for the AdS 5 x S 5 mirror. arXiv:0901.1417 [hep-th]

  26. Juttner G., Klumper A., Suzuki J.: From fusion hierarchy to excited state TBA. Nucl. Phys. B 512, 581 (1998) arXiv:hep-th/9707074

    Article  MathSciNet  ADS  Google Scholar 

  27. Aharony O., Bergman O., Jafferis D.L., Maldacena J.: N = 6 superconformal Chern–Simons-matter theories, M2-branes and their gravity duals. JHEP 0810, 091 (2008) [arXiv:0806.1218 [hep-th]]

    Article  MathSciNet  ADS  Google Scholar 

  28. Minahan J.A., Zarembo K.: The Bethe ansatz for superconformal Chern–Simons. JHEP 0809, 040 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  29. Gromov, N., Vieira, P.: The AdS4/CFT3 algebraic curve. arXiv:0807.0437 [hep-th]

  30. Gromov, N., Vieira, P.: The all loop AdS4/CFT3 Bethe ansatz. arXiv:0807.0777 [hep-th]

  31. Bombardelli, D., Fioravanti, D., Tateo, R.: Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal. arXiv:0902.3930 [hep-th]

  32. Arutyunov G., Frolov S.: Thermodynamic Bethe Ansatz for the AdS 5 × S 5 mirror model. JHEP 0905, 068 (2009) arXiv:0903.0141 [hep-th]

    Article  ADS  Google Scholar 

  33. Arutyunov, G., Frolov, S.: The Dressing Factor and Crossing Equations. arXiv:0904. 4575 [hep-th]

Download references

Author information

Authors and Affiliations

  1. DESY Theory, Hamburg, Germany

    Nikolay Gromov

  2. II. Institut für Theoretische Physik Universität, Hamburg, Germany

    Nikolay Gromov

  3. St.Petersburg INP, St.Petersburg, Russia

    Nikolay Gromov

  4. Ecole Normale Superieure, LPT, 75231, Paris Cedex-5, France

    Vladimir Kazakov

  5. l’Université Paris-VI, Paris, France

    Andrii Kozak

  6. Max-Planck-Institut für Gravitationphysik, Albert-Einstein-Institut, 14476, Potsdam, Germany

    Pedro Vieira

Authors
  1. Nikolay Gromov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vladimir Kazakov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Andrii Kozak
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Pedro Vieira
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nikolay Gromov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gromov, N., Kazakov, V., Kozak, A. et al. Exact Spectrum of Anomalous Dimensions of Planar N = 4 Supersymmetric Yang–Mills Theory: TBA and excited states. Lett Math Phys 91, 265–287 (2010). https://doi.org/10.1007/s11005-010-0374-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11005-010-0374-8

Mathematics Subject Classification (2000)

Keywords

Search

Navigation