Advertisement

Reformulating the TBA equations for the quark anti-quark potential and their two loop expansion

  • Zoltán BajnokEmail author
  • János Balog
  • Diego H. Correa
  • Árpád Hegedűs
  • Fidel I. Schaposnik Massolo
  • Gábor Zsolt Tóth
Open Access
Article

Abstract

The boundary thermodynamic Bethe Ansatz (BTBA) equations introduced in [1, 2] to describe the cusp anomalous dimension contain imaginary chemical potentials and singular boundary fugacities, which make its systematic expansion problematic. We propose an alternative formulation based on real chemical potentials and additional source terms. We expand our equations to double wrapping order and find complete agreement with the direct two-loop gauge theory computation of the cusp anomalous dimension.

Keywords

AdS-CFT Correspondence 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]
    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].ADSCrossRefGoogle Scholar
  2. [2]
    N. Drukker, Integrable Wilson loops, JHEP 10 (2013) 135 [arXiv:1203.1617] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  3. [3]
    G. Arutyunov and S. Frolov, String hypothesis for the AdS 5 × S 5 mirror, JHEP 03 (2009) 152 [arXiv:0901.1417] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  4. [4]
    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].ADSCrossRefMathSciNetGoogle Scholar
  5. [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].ADSMathSciNetGoogle Scholar
  6. [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].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  7. [7]
    G. Arutyunov and S. Frolov, Thermodynamic Bethe Ansatz for the AdS 5 × S 5 Mirror Model, JHEP 05 (2009) 068 [arXiv:0903.0141] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  8. [8]
    G. Arutyunov and S. Frolov, Simplified TBA equations of the AdS 5 × S 5 mirror model, JHEP 11 (2009) 019 [arXiv:0907.2647] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  9. [9]
    S.J. van Tongeren, Integrability of the AdS 5 × S 5 superstring and its deformations, arXiv:1310.4854 [INSPIRE].
  10. [10]
    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].ADSCrossRefGoogle Scholar
  11. [11]
    Z. Bajnok, C. Rim and A. Zamolodchikov, Sinh-Gordon boundary TBA and boundary Liouville reflection amplitude, Nucl. Phys. B 796 (2008) 622 [arXiv:0710.4789] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  12. [12]
    N. Gromov, V. Kazakov and P. Vieira, Exact Spectrum of Planar \( \mathcal{N} \) = 4 Supersymmetric Yang-Mills Theory: Konishi Dimension at Any Coupling, Phys. Rev. Lett. 104 (2010) 211601 [arXiv:0906.4240] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  13. [13]
    A.M. Polyakov, Gauge Fields as Rings of Glue, Nucl. Phys. B 164 (1980) 171 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  14. [14]
    G.P. Korchemsky and A.V. Radyushkin, Infrared factorization, Wilson lines and the heavy quark limit, Phys. Lett. B 279 (1992) 359 [hep-ph/9203222] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    D. Correa, J. Henn, J. Maldacena and A. Sever, The cusp anomalous dimension at three loops and beyond, JHEP 05 (2012) 098 [arXiv:1203.1019] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  16. [16]
    J.M. Henn and T. Huber, The four-loop cusp anomalous dimension in \( \mathcal{N} \) = 4 super Yang-Mills and analytic integration techniques for Wilson line integrals, JHEP 09 (2013) 147 [arXiv:1304.6418] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  17. [17]
    G. Arutyunov, S. Frolov and R. Suzuki, Exploring the mirror TBA, JHEP 05 (2010) 031 [arXiv:0911.2224] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  18. [18]
    A. Cavaglia, D. Fioravanti and R. Tateo, Extended Y-system for the AdS 5 /CFT 4 correspondence, Nucl. Phys. B 843 (2011) 302 [arXiv:1005.3016] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  19. [19]
    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].ADSCrossRefGoogle Scholar
  20. [20]
    Z. Bajnok, L. Palla and G. Takács, Boundary one-point function, Casimir energy and boundary state formalism in D + 1 dimensional QFT, Nucl. Phys. B 772 (2007) 290 [hep-th/0611176] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    D. Correa, J. Henn, J. Maldacena and A. Sever, An exact formula for the radiation of a moving quark in N = 4 super Yang-Mills, JHEP 06 (2012) 048 [arXiv:1202.4455] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  22. [22]
    B. Fiol, B. Garolera and A. Lewkowycz, Exact results for static and radiative fields of a quark in N = 4 super Yang-Mills, JHEP 05 (2012) 093 [arXiv:1202.5292] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    N. Gromov and A. Sever, Analytic Solution of Bremsstrahlung TBA, JHEP 11 (2012) 075 [arXiv:1207.5489] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  24. [24]
    N. Gromov, V. Kazakov, S. Leurent and D. Volin, Quantum spectral curve for AdS 5 /CFT 4, Phys. Rev. Lett. 112 (2014) 011602 [arXiv:1305.1939] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    N. Gromov, F. Levkovich-Maslyuk and G. Sizov, Analytic Solution of Bremsstrahlung TBA II: Turning on the Sphere Angle, JHEP 10 (2013) 036 [arXiv:1305.1944] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  26. [26]
    N. Beisert, B. Eden and M. Staudacher, Transcendentality and Crossing, J. Stat. Mech. 0701 (2007) P01021 [hep-th/0610251] [INSPIRE].Google Scholar
  27. [27]
    G. Arutyunov and S. Frolov, The Dressing Factor and Crossing Equations, J. Phys. A 42 (2009) 425401 [arXiv:0904.4575] [INSPIRE].ADSMathSciNetGoogle Scholar
  28. [28]
    A. LeClair, G. Mussardo, H. Saleur and S. Skorik, Boundary energy and boundary states in integrable quantum field theories, Nucl. Phys. B 453 (1995) 581 [hep-th/9503227] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  29. [29]
    P. Dorey, A. Pocklington, R. Tateo and G. Watts, TBA and TCSA with boundaries and excited states, Nucl. Phys. B 525 (1998) 641 [hep-th/9712197] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Zoltán Bajnok
    • 1
    Email author
  • János Balog
    • 1
  • Diego H. Correa
    • 2
  • Árpád Hegedűs
    • 1
  • Fidel I. Schaposnik Massolo
    • 2
  • Gábor Zsolt Tóth
    • 1
  1. 1.MTA Lendület Holographic QFT GroupWigner Research CentreBudapest 114Hungary
  2. 2.Instituto de Física La Plata, CONICETUniversidad Nacional de La PlataLa PlataArgentina

Personalised recommendations