Skip to main content
SpringerLink
Log in

An exact formula for the radiation of a moving quark in \(\mathcal{N} = 4\) super Yang Mills

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

Abstract

We derive an exact formula for the cusp anomalous dimension at small angles. This is done by relating the latter to the computation of certain 1/8 BPS Wilson loops which was performed by supersymmetric localization. This function of the coupling also determines the power emitted by a moving quark in \(\mathcal{N} = 4\) super Yang Mills, as well as the coefficient of the two point function of the displacement operator on the Wilson loop. By a similar method we compute the near BPS expansion of the generalized cusp anomalous dimension.

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. 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 

  2. 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 

  3. N. Drukker, S. Giombi, R. Ricci and D. Trancanelli, On the D3-brane description of some 1/4 BPS Wilson loops, JHEP 04 (2007) 008 [hep-th/0612168] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  4. N. Drukker, S. Giombi, R. Ricci and D. Trancanelli, More supersymmetric Wilson loops, Phys. Rev. D 76 (2007) 107703 [arXiv:0704.2237] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  5. N. Drukker, S. Giombi, R. Ricci and D. Trancanelli, Wilson loops: from four-dimensional SYM to two-dimensional YM, Phys. Rev. D 77 (2008) 047901 [arXiv:0707.2699] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  6. A. Bassetto, L. Griguolo, F. Pucci and D. Seminara, Supersymmetric Wilson loops at two loops, JHEP 06 (2008) 083 [arXiv:0804.3973] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. D. Young, BPS Wilson loops on S 2 at higher loops, JHEP 05 (2008) 077 [arXiv:0804.4098] [INSPIRE].

    Article  ADS  Google Scholar 

  8. V. Pestun, Localization of the four-dimensional N = 4 SYM to a two-sphere and 1/8 BPS Wilson loops, arXiv:0906.0638 [INSPIRE].

  9. S. Giombi, V. Pestun and R. Ricci, Notes on supersymmetric Wilson loops on a two-sphere, JHEP 07 (2010) 088 [arXiv:0905.0665] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. S. Giombi and V. Pestun, Correlators of local operators and 1/8 BPS Wilson loops on S 2 from 2D YM and matrix models, JHEP 10 (2010) 033 [arXiv:0906.1572] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. 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 

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

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

  14. A.M. Polyakov, Gauge fields as rings of glue, Nucl. Phys. B 164 (1980) 171 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  15. G. Korchemsky and A. Radyushkin, Infrared factorization, Wilson lines and the heavy quark limit, Phys. Lett. B 279 (1992) 359 [hep-ph/9203222] [INSPIRE].

    Article  ADS  Google Scholar 

  16. T. Becher and M. Neubert, Infrared singularities of QCD amplitudes with massive partons, Phys. Rev. D 79 (2009) 125004 [Erratum ibid. D 80 (2009) 109901] [arXiv:0904.1021] [INSPIRE].

    ADS  Google Scholar 

  17. J.M. Henn, S.G. Naculich, H.J. Schnitzer and M. Spradlin, Higgs-regularized three-loop four-gluon amplitude in N = 4 SYM: exponentiation and Regge limits, JHEP 04 (2010) 038 [arXiv:1001.1358] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  18. G. Korchemsky and A. Radyushkin, Renormalization of the Wilson loops beyond the leading order, Nucl. Phys. B 283 (1987) 342 [INSPIRE].

    Article  ADS  Google Scholar 

  19. N. Beisert, B. Eden and M. Staudacher, Transcendentality and crossing, J. Stat. Mech. 0701 (2007) P01021 [hep-th/0610251] [INSPIRE].

    Article  Google Scholar 

  20. A.M. Polyakov and V.S. Rychkov, Gauge field strings duality and the loop equation, Nucl. Phys. B 581 (2000) 116 [hep-th/0002106] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. G.W. Semenoff and D. Young, Wavy Wilson line and AdS/CFT, Int. J. Mod. Phys. A 20 (2005)2833 [hep-th/0405288] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. N. Drukker, D.J. Gross and H. Ooguri, Wilson loops and minimal surfaces, Phys. Rev. D 60 (1999)125006 [hep-th/9904191] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  24. 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 

  25. K. Zarembo, Supersymmetric Wilson loops, Nucl. Phys. B 643 (2002) 157 [hep-th/0205160] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. D. Correa, J. Maldacena and A. Sever, The quark anti-quark potential and the cusp anomalous dimension from a TBA equation, arXiv:1203.1913 [INSPIRE].

  27. N. Beisert et al., Review of AdS/CFT integrability: an overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. S. Giombi and V. Pestun, The 1/2 BPS ’t Hooft loops in N = 4 SYM as instantons in 2D Yang-Mills, arXiv:0909.4272 [INSPIRE].

  29. D. Correa, J. Henn, J. Maldacena and A. Sever, The cusp anomalous dimension at three loops and beyond, arXiv:1203.1019 [INSPIRE].

  30. L.F. Alday and J. Maldacena, Comments on gluon scattering amplitudes via AdS/CFT, JHEP 11 (2007) 068 [arXiv:0710.1060] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. 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].

    Article  ADS  Google Scholar 

  32. 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 

  33. H. Dorn, Renormalization of path ordered phase factors and related hadron operators in gauge field theories, Fortsch. Phys. 34 (1986) 11 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  34. N. Drukker and S. Kawamoto, Small deformations of supersymmetric Wilson loops and open spin-chains, JHEP 07 (2006) 024 [hep-th/0604124] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  35. 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].

    ADS  Google Scholar 

  36. 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 

  37. D. Gaiotto, private communication.

  38. B. Basso, An exact slope for AdS/CFT, arXiv:1109.3154 [INSPIRE].

  39. T. Nishioka and T. Takayanagi, On type IIA Penrose limit and N = 6 Chern-Simons theories, JHEP 08 (2008) 001 [arXiv:0806.3391] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. D. Gaiotto, S. Giombi and X. Yin, Spin chains in N = 6 superconformal Chern-Simons-matter theory, JHEP 04 (2009) 066 [arXiv:0806.4589] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  41. G. Grignani, T. Harmark and M. Orselli, The SU(2) × SU(2) sector in the string dual of N = 6 superconformal Chern-Simons theory, Nucl. Phys. B 810 (2009)115 [arXiv:0806.4959] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  42. N. Gromov and P. Vieira, The all loop AdS4/CF T 3 Bethe ansatz, JHEP 01 (2009) 016 [arXiv:0807.0777] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instituto de Física La Plata, Universidad Nacional de La Plata, C.C. 67, 1900, La Plata, Argentina

    Diego Correa

  2. School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, 08540, U.S.A.

    Johannes Henn, Juan Maldacena & Amit Sever

  3. Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2J 2W9, Canada

    Amit Sever

Authors
  1. Diego Correa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Johannes Henn
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Juan Maldacena
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Amit Sever
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Amit Sever.

Additional information

ArXiv ePrint: 1202.4455

Rights and permissions

Reprints and permissions

About this article

Cite this article

Correa, D., Henn, J., Maldacena, J. et al. An exact formula for the radiation of a moving quark in \(\mathcal{N} = 4\) super Yang Mills. J. High Energ. Phys. 2012, 48 (2012). https://doi.org/10.1007/JHEP06(2012)048

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP06(2012)048

Keywords

Search

Navigation