Exact results for static and radiative fields of a quark in \( \mathcal{N} = 4 \) super Yang-Mills

  • Bartomeu Fiol
  • Blai Garolera
  • Aitor Lewkowycz


In this work (which supersedes our previous preprint [1]) we determine the expectation value of the \( \mathcal{N} = 4 \) SU(N) SYM Lagrangian density operator in the presence of an infinitely heavy static particle in the symmetric representation of SU(N), by means of a D3-brane probe computation. The result that we obtain coincides with two previous computations of different observables, up to kinematical factors. We argue that these agreements go beyond the D-brane probe approximation, which leads us to propose an exact formula for the expectation value of various operators. In particular, we provide an expression for the total energy loss by radiation of a heavy particle in the fundamental representation.


Supersymmetric gauge theory AdS-CFT Correspondence 


  1. [1]
    B. Fiol, B. Garolera and A. Lewkowycz, Gluonic fields of a static particle to all orders in 1/N , arXiv:1112.2345 [INSPIRE].
  2. [2]
    F. Dolan and H. Osborn, On short and semi-short representations for four-dimensional superconformal symmetry, Annals Phys. 307 (2003) 41 [hep-th/0209056] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  3. [3]
    S. Lee, S. Minwalla, M. Rangamani and N. Seiberg, Three point functions of chiral operators in D = 4, N = 4 SYM at large-N, Adv. Theor. Math. Phys. 2 (1998) 697 [hep-th/9806074] [INSPIRE].MathSciNetMATHGoogle Scholar
  4. [4]
    M. Baggio, J. de Boer and K. Papadodimas, A non-renormalization theorem for chiral primary 3-point functions, arXiv:1203.1036 [INSPIRE].
  5. [5]
    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
  6. [6]
    N. Drukker and D.J. Gross, An exact prediction of N = 4 SUSYM theory for string theory, J. Math. Phys. 42 (2001) 2896 [hep-th/0010274] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  7. [7]
    V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, arXiv:0712.2824 [INSPIRE].
  8. [8]
    N. Drukker, 1/4 BPS circular loops, unstable world-sheet instantons and the matrix model, JHEP 09 (2006) 004 [hep-th/0605151] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    G.W. Semenoff and K. Zarembo, More exact predictions of SUSYM for string theory, Nucl. Phys. B 616 (2001) 34 [hep-th/0106015] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  10. [10]
    K. Okuyama and G.W. Semenoff, Wilson loops in N = 4 SYM and fermion droplets, JHEP 06 (2006) 057 [hep-th/0604209] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  11. [11]
    S. Giombi, R. Ricci and D. Trancanelli, Operator product expansion of higher rank Wilson loops from D-branes and matrix models, JHEP 10 (2006) 045 [hep-th/0608077] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    E. D’Hoker and D.Z. Freedman, Supersymmetric gauge theories and the AdS/CFT correspondence, hep-th/0201253 [INSPIRE].
  14. [14]
    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, arXiv:1202.4455 [INSPIRE].
  15. [15]
    B. Fiol and B. Garolera, Energy loss of an infinitely massive half-Bogomol’nyi-Prasad-Sommerfeld particle by radiation to all orders in 1/N, Phys. Rev. Lett. 107 (2011) 151601 [arXiv:1106.5418] [INSPIRE].ADSCrossRefGoogle 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].MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  18. [18]
    U.H. Danielsson, E. Keski-Vakkuri and M. Kruczenski, Vacua, propagators and holographic probes in AdS/CFT, JHEP 01 (1999) 002 [hep-th/9812007] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    C.G. Callan Jr. and A. Guijosa, Undulating strings and gauge theory waves, Nucl. Phys. B 565 (2000) 157 [hep-th/9906153] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  20. [20]
    C. Athanasiou, P.M. Chesler, H. Liu, D. Nickel and K. Rajagopal, Synchrotron radiation in strongly coupled conformal field theories, Phys. Rev. D 81 (2010) 126001 [Erratum ibid. D 84 (2011) 069901] [arXiv:1001.3880] [INSPIRE].
  21. [21]
    Y. Hatta, E. Iancu, A. Mueller and D. Triantafyllopoulos, Aspects of the UV/IR correspondence: energy broadening and string fluctuations, JHEP 02 (2011) 065 [arXiv:1011.3763] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    Y. Hatta, E. Iancu, A. Mueller and D. Triantafyllopoulos, Radiation by a heavy quark in N = 4 SYM at strong coupling, Nucl. Phys. B 850 (2011) 31 [arXiv:1102.0232] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  23. [23]
    R. Baier, On radiation by a heavy quark in N = 4 SYM, arXiv:1107.4250 [INSPIRE].
  24. [24]
    M. Chernicoff, A. Guijosa and J.F. Pedraza, The gluonic field of a heavy quark in conformal field theories at strong coupling, JHEP 10 (2011) 041 [arXiv:1106.4059] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    A. Mikhailov, Nonlinear waves in AdS/CFT correspondence, hep-th/0305196 [INSPIRE].
  26. [26]
    S. Förste, D. Ghoshal and S. Theisen, Stringy corrections to the Wilson loop in N = 4 super Yang-Mills theory, JHEP 08 (1999) 013 [hep-th/9903042] [INSPIRE].CrossRefGoogle Scholar
  27. [27]
    N. Drukker, D.J. Gross and A.A. Tseytlin, Green-Schwarz string in AdS 5 × S 5 : semiclassical partition function, JHEP 04 (2000) 021 [hep-th/0001204] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  28. [28]
    V. Forini, Quark-antiquark potential in AdS at one loop, JHEP 11 (2010) 079 [arXiv:1009.3939] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    N. Drukker and V. Forini, Generalized quark-antiquark potential at weak and strong coupling, JHEP 06 (2011) 131 [arXiv:1105.5144] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    J. Gomis and F. Passerini, Holographic Wilson loops, JHEP 08 (2006) 074 [hep-th/0604007] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  31. [31]
    J. Gomis and F. Passerini, Wilson Loops as D3-branes, JHEP 01 (2007) 097 [hep-th/0612022] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  32. [32]
    S. Yamaguchi, Wilson loops of anti-symmetric representation and D5-branes, JHEP 05 (2006) 037 [hep-th/0603208] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    S.A. Hartnoll and S.P. Kumar, Multiply wound Polyakov loops at strong coupling, Phys. Rev. D 74 (2006) 026001 [hep-th/0603190] [INSPIRE].MathSciNetADSGoogle Scholar
  34. [34]
    S.A. Hartnoll, Two universal results for Wilson loops at strong coupling, Phys. Rev. D 74 (2006) 066006 [hep-th/0606178] [INSPIRE].MathSciNetADSGoogle Scholar
  35. [35]
    C.G. Callan Jr., A. Guijosa and K.G. Savvidy, Baryons and string creation from the five-brane world volume action, Nucl. Phys. B 547 (1999) 127 [hep-th/9810092] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  36. [36]
    J. Camino, A. Paredes and A. Ramallo, Stable wrapped branes, JHEP 05 (2001) 011 [hep-th/0104082] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  37. [37]
    S.A. Hartnoll and S.P. Kumar, Higher rank Wilson loops from a matrix model, JHEP 08 (2006) 026 [hep-th/0605027] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  38. [38]
    M. Chernicoff and A. Guijosa, Energy loss of gluons, baryons and k-quarks in an N = 4 SYM plasma, JHEP 02 (2007) 084 [hep-th/0611155] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  39. [39]
    W. Mueck, The Polyakov loop of anti-symmetric representations as a quantum impurity model, Phys. Rev. D 83 (2011) 066006 [Erratum ibid. D 84 (2011) 129903] [arXiv:1012.1973] [INSPIRE].
  40. [40]
    S. Harrison, S. Kachru and G. Torroba, A maximally supersymmetric Kondo model, arXiv:1110.5325 [INSPIRE].
  41. [41]
    N. Drukker and B. Fiol, All-genus calculation of Wilson loops using D-branes, JHEP 02 (2005) 010 [hep-th/0501109] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  42. [42]
    I.R. Klebanov, World volume approach to absorption by nondilatonic branes, Nucl. Phys. B 496 (1997) 231 [hep-th/9702076] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  43. [43]
    I.R. Klebanov, W. Taylor and M. Van Raamsdonk, Absorption of dilaton partial waves by D3-branes, Nucl. Phys. B 560 (1999) 207 [hep-th/9905174] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    D.E. Berenstein, R. Corrado, W. Fischler and J.M. Maldacena, The operator product expansion for Wilson loops and surfaces in the large-N limit, Phys. Rev. D 59 (1999) 105023 [hep-th/9809188] [INSPIRE].MathSciNetADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  1. 1.Departament de Física Fonamental i Institut de Ciències del CosmosUniversitat de BarcelonaBarcelonaSpain
  2. 2.Perimeter Institute for Theoretical PhysicsWaterlooCanada

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