Skip to main content
SpringerLink
Log in

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

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

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.

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. B. Fiol, B. Garolera and A. Lewkowycz, Gluonic fields of a static particle to all orders in 1/N , arXiv:1112.2345 [INSPIRE].

  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].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  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].

    MathSciNet  MATH  Google Scholar 

  4. M. Baggio, J. de Boer and K. Papadodimas, A non-renormalization theorem for chiral primary 3-point functions, arXiv:1203.1036 [INSPIRE].

  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].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, arXiv:0712.2824 [INSPIRE].

  8. N. Drukker, 1/4 BPS circular loops, unstable world-sheet instantons and the matrix model, JHEP 09 (2006) 004 [hep-th/0605151] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

  10. K. Okuyama and G.W. Semenoff, Wilson loops in N = 4 SYM and fermion droplets, JHEP 06 (2006) 057 [hep-th/0604209] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

  13. E. D’Hoker and D.Z. Freedman, Supersymmetric gauge theories and the AdS/CFT correspondence, hep-th/0201253 [INSPIRE].

  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. 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].

    Article  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

  17. J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  19. C.G. Callan Jr. and A. Guijosa, Undulating strings and gauge theory waves, Nucl. Phys. B 565 (2000) 157 [hep-th/9906153] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  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. 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].

    Article  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

  23. R. Baier, On radiation by a heavy quark in N = 4 SYM, arXiv:1107.4250 [INSPIRE].

  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].

    Article  ADS  Google Scholar 

  25. A. Mikhailov, Nonlinear waves in AdS/CFT correspondence, hep-th/0305196 [INSPIRE].

  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].

    Article  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

  28. V. Forini, Quark-antiquark potential in AdS at one loop, JHEP 11 (2010) 079 [arXiv:1009.3939] [INSPIRE].

    Article  ADS  Google Scholar 

  29. N. Drukker and V. Forini, Generalized quark-antiquark potential at weak and strong coupling, JHEP 06 (2011) 131 [arXiv:1105.5144] [INSPIRE].

    Article  ADS  Google Scholar 

  30. J. Gomis and F. Passerini, Holographic Wilson loops, JHEP 08 (2006) 074 [hep-th/0604007] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. J. Gomis and F. Passerini, Wilson Loops as D3-branes, JHEP 01 (2007) 097 [hep-th/0612022] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  32. S. Yamaguchi, Wilson loops of anti-symmetric representation and D5-branes, JHEP 05 (2006) 037 [hep-th/0603208] [INSPIRE].

    Article  ADS  Google Scholar 

  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].

    MathSciNet  ADS  Google Scholar 

  34. S.A. Hartnoll, Two universal results for Wilson loops at strong coupling, Phys. Rev. D 74 (2006) 066006 [hep-th/0606178] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

  36. J. Camino, A. Paredes and A. Ramallo, Stable wrapped branes, JHEP 05 (2001) 011 [hep-th/0104082] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  37. S.A. Hartnoll and S.P. Kumar, Higher rank Wilson loops from a matrix model, JHEP 08 (2006) 026 [hep-th/0605027] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

  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. S. Harrison, S. Kachru and G. Torroba, A maximally supersymmetric Kondo model, arXiv:1110.5325 [INSPIRE].

  41. N. Drukker and B. Fiol, All-genus calculation of Wilson loops using D-branes, JHEP 02 (2005) 010 [hep-th/0501109] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  42. I.R. Klebanov, World volume approach to absorption by nondilatonic branes, Nucl. Phys. B 496 (1997) 231 [hep-th/9702076] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  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].

    MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departament de Física Fonamental i Institut de Ciències del Cosmos, Universitat de Barcelona, Martí i Franquès 1, 08028, Barcelona, Catalonia, Spain

    Bartomeu Fiol & Blai Garolera

  2. Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5, Canada

    Aitor Lewkowycz

Authors
  1. Bartomeu Fiol
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Blai Garolera
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Aitor Lewkowycz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bartomeu Fiol.

Additional information

ArXiv ePrint: 1202.5292

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fiol, B., Garolera, B. & Lewkowycz, A. Exact results for static and radiative fields of a quark in \( \mathcal{N} = 4 \) super Yang-Mills. J. High Energ. Phys. 2012, 93 (2012). https://doi.org/10.1007/JHEP05(2012)093

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP05(2012)093

Keywords

Search

Navigation