Journal of High Energy Physics

, 2012:155 | Cite as

NLL resummation for the static potential in \( \mathcal{N}=4 \) SYM theory

  • Maximilian StahlhofenEmail author
Open Access


We determine the complete NLL running of the static potential associated with the locally 1/2 BPS Wilson loop in \( \mathcal{N}=4 \) supersymmetric Yang-Mills theory. We present results for the SU(N c) singlet as well as for the adjoint configuration and arbitrary N c at weak coupling. In order to derive the respective anomalous dimensions we perform a two-loop calculation in the \( \mathcal{N}=4 \) supersymmetric version of the effective field theory pNRQCD. In addition we confirm the recently obtained fixed-order result for the singlet static potential generated exclusively by ladder diagrams to the third order in the t‘Hooft coupling. We also give an explicit expression for the logarithmic contribution of all non-ladder diagrams at this order.


Wilson ’t Hooft and Polyakov loops Extended Supersymmetry Resummation Supersymmetric Effective Theories 


  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].MathSciNetADSzbMATHGoogle Scholar
  2. [2]
    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].MathSciNetADSGoogle Scholar
  3. [3]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].MathSciNetADSzbMATHGoogle Scholar
  4. [4]
    N. Beisert et al., Review of AdS/CFT integrability: an overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    N. Drukker, D.J. Gross and H. Ooguri, Wilson loops and minimal surfaces, Phys. Rev. D 60 (1999) 125006 [hep-th/9904191] [INSPIRE].MathSciNetADSGoogle Scholar
  6. [6]
    Y. Schroder, The static potential in QCD, DESY-THESIS-1999-021, DESY, Hamburg Germany (1999) [INSPIRE].Google Scholar
  7. [7]
    F. Gliozzi, J. Scherk and D.I. Olive, Supersymmetry, supergravity theories and the dual spinor model, Nucl. Phys. B 122 (1977) 253 [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    L. Brink, J.H. Schwarz and J. Scherk, Supersymmetric Yang-Mills theories, Nucl. Phys. B 121 (1977) 77 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    S.-X. Chu, D. Hou and H.-C. Ren, The subleading term of the strong coupling expansion of the heavy-quark potential in a N = 4 super Yang-Mills vacuum, JHEP 08 (2009) 004 [arXiv:0905.1874] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  10. [10]
    V. Forini, Quark-antiquark potential in AdS at one loop, JHEP 11 (2010) 079 [arXiv:1009.3939] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].MathSciNetADSzbMATHCrossRefGoogle Scholar
  12. [12]
    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].MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    N. Drukker and V. Forini, Generalized quark-antiquark potential at weak and strong coupling, JHEP 06 (2011) 131 [arXiv:1105.5144] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    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].ADSCrossRefGoogle Scholar
  15. [15]
    J.M. Henn and T. Huber, Systematics of the cusp anomalous dimension, JHEP 11 (2012) 058 [arXiv:1207.2161] [INSPIRE].CrossRefGoogle Scholar
  16. [16]
    J. Erickson, G. Semenoff, R. Szabo and K. Zarembo, Static potential in N = 4 supersymmetric Yang-Mills theory, Phys. Rev. D 61 (2000) 105006 [hep-th/9911088] [INSPIRE].MathSciNetADSGoogle Scholar
  17. [17]
    J. Erickson, G. Semenoff and K. Zarembo, Wilson loops in N = 4 supersymmetric Yang-Mills theory, Nucl. Phys. B 582 (2000) 155 [hep-th/0003055] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  18. [18]
    D. Bykov and K. Zarembo, Ladders for Wilson loops beyond leading order, JHEP 09 (2012) 057 [arXiv:1206.7117] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    T. Appelquist, M. Dine and I. Muzinich, The static limit of quantum chromodynamics, Phys. Rev. D 17 (1978) 2074 [INSPIRE].ADSGoogle Scholar
  20. [20]
    N. Brambilla, A. Pineda, J. Soto and A. Vairo, The infrared behavior of the static potential in perturbative QCD, Phys. Rev. D 60 (1999) 091502 [hep-ph/9903355] [INSPIRE].ADSGoogle Scholar
  21. [21]
    A. Pineda and M. Stahlhofen, The QCD static potential in D < 4 dimensions at weak coupling, Phys. Rev. D 81 (2010) 074026 [arXiv:1002.1965] [INSPIRE].ADSGoogle Scholar
  22. [22]
    A. Pineda and J. Soto, Effective field theory for ultrasoft momenta in NRQCD and NRQED, Nucl. Phys. Proc. Suppl. 64 (1998) 428 [hep-ph/9707481] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    N. Brambilla, A. Pineda, J. Soto and A. Vairo, Potential NRQCD: an effective theory for heavy quarkonium, Nucl. Phys. B 566 (2000) 275 [hep-ph/9907240] [INSPIRE].CrossRefGoogle Scholar
  24. [24]
    A. Pineda, The static potential in N = 4 supersymmetric Yang-Mills at weak coupling, Phys. Rev. D 77 (2008) 021701 [arXiv:0709.2876] [INSPIRE].MathSciNetADSGoogle Scholar
  25. [25]
    A. Pineda and M. Stahlhofen, The static hybrid potential in D dimensions at short distances, Phys. Rev. D 84 (2011) 034016 [arXiv:1105.4356] [INSPIRE].ADSGoogle Scholar

Copyright information

© SISSA 2012

Authors and Affiliations

  1. 1.University of Vienna, Faculty of PhysicsWienAustria
  2. 2.DESY Theory GroupHamburgGermany

Personalised recommendations