Cusp anomalous dimension and rotating open strings in AdS/CFT

  • R. Espíndola
  • J. Antonio García
Open Access
Regular Article - Theoretical Physics


In the context of AdS/CFT we provide analytical support for the proposed duality between a Wilson loop with a cusp, the cusp anomalous dimension, and the meson model constructed from a rotating open string with high angular momentum. This duality was previously studied using numerical tools in [1]. Our result implies that the minimum of the profile function of the minimal area surface dual to the Wilson loop, is related to the inverse of the bulk penetration of the dual string that hangs from the quark-anti-quark pair (meson) in the gauge theory.


AdS-CFT Correspondence Gauge Symmetry String Duality 


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.


  1. [1]
    S. Caron-Huot and J.M. Henn, Solvable Relativistic Hydrogenlike System in Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 113 (2014) 161601 [arXiv:1408.0296] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    J.M. Henn, Dual conformal symmetry at loop level: massive regularization, J. Phys. A 44 (2011) 454011 [arXiv:1103.1016] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  3. [3]
    V.N. Gribov, The Theory of Complex Angular Momenta: Gribov Lectures on Theoretical Physics, Cambridge University Press, Cambridge U.K. (2003).CrossRefzbMATHGoogle Scholar
  4. [4]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    J.M. Henn, S.G. Naculich, H.J. Schnitzer and M. Spradlin, Higgs-regularized three-loop four-gluon amplitude in \( \mathcal{N}=4 \) SYM: exponentiation and Regge limits, JHEP 04 (2010) 038 [arXiv:1001.1358] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    M. Kruczenski, D. Mateos, R.C. Myers and D.J. Winters, Meson spectroscopy in AdS/CFT with flavor, JHEP 07 (2003) 049 [hep-th/0304032] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    N.R.F. Braga and E. Iancu, Anomalous dimensions from rotating open strings in AdS/CFT, JHEP 08 (2014) 104 [arXiv:1405.7388] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  11. [11]
    A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    I. Kirsch and D. Vaman, The D3/D7 background and flavor dependence of Regge trajectories, Phys. Rev. D 72 (2005) 026007 [hep-th/0505164] [INSPIRE].ADSMathSciNetGoogle Scholar
  13. [13]
    J. Erdmenger, N. Evans, I. Kirsch and E. Threlfall, Mesons in Gauge/Gravity Duals — A Review, Eur. Phys. J. A 35 (2008) 81 [arXiv:0711.4467] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    S.S. Gubser, I.R. Klebanov and A.M. Polyakov, A semiclassical limit of the gauge/string correspondence, Nucl. Phys. B 636 (2002) 99 [hep-th/0204051] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  15. [15]
    J.M. Maldacena, Wilson loops in large N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    S.-J. Rey and J.-T. Yee, Macroscopic strings as heavy quarks in large N gauge theory and anti-de Sitter supergravity, Eur. Phys. J. C 22 (2001) 379 [hep-th/9803001] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  17. [17]
    H. Dorn, Wilson loops at strong coupling for curved contours with cusps, J. Phys. A 49 (2016) 145402 [arXiv:1509.00222] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  18. [18]
    N. Drukker, D.J. Gross and H. Ooguri, Wilson loops and minimal surfaces, Phys. Rev. D 60 (1999) 125006 [hep-th/9904191] [INSPIRE].ADSMathSciNetGoogle Scholar
  19. [19]
    M. Kruczenski, A note on twist two operators in \( \mathcal{N}=4 \) SYM and Wilson loops in Minkowski signature, JHEP 12 (2002) 024 [hep-th/0210115] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  20. [20]
    D. Correa, J. Henn, J. Maldacena and A. Sever, An exact formula for the radiation of a moving quark in \( \mathcal{N}=4 \) super Yang-Mills, JHEP 06 (2012) 048 [arXiv:1202.4455] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    T. Banks and T.J. Torres, Two Point Padé Approximants and Duality, arXiv:1307.3689 [INSPIRE].
  22. [22]
    V.I. Yukalov and S. Gluzman, Self-similar interpolation in high-energy physics, Phys. Rev. D 91 (2015) 125023 [arXiv:1506.09022] [INSPIRE].ADSMathSciNetGoogle Scholar
  23. [23]
    R. Espíndola and J. Antonio García, Cusp anomalous dimension and rotating strings in symmetric and antisymmetric representations, work in progress.Google Scholar
  24. [24]
    B. Fiol, A. Güijosa and J.F. Pedraza, Branes from Light: Embeddings and Energetics for Symmetric k-Quarks in \( \mathcal{N}=4 \) SYM, JHEP 01 (2015) 149 [arXiv:1410.0692] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    D.H. Correa, F.I. Schaposnik Massolo and D. Trancanelli, Cusped Wilson lines in symmetric representations, JHEP 08 (2015) 091 [arXiv:1506.01680] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    T. Hirata and T. Takayanagi, AdS/CFT and strong subadditivity of entanglement entropy, JHEP 02 (2007) 042 [hep-th/0608213] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
    P. Bueno, R.C. Myers and W. Witczak-Krempa, Universal corner entanglement from twist operators, JHEP 09 (2015) 091 [arXiv:1507.06997] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Departamento de Física de Altas Energías, Instituto de Ciencias NuclearesUniversidad Nacional Autónoma de MéxicoCiudad de MéxicoMéxico

Personalised recommendations