Skip to main content
SpringerLink
Log in

Wilson Loops in Exact Holographic RG Flows at Zero and Finite Temperatures

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We study rectangular timelike Wilson loops at long distances in the exact renormalization group flow in the context of the holographic duality. We consider the five-dimensional holographic model with an exponential dilaton potential. To probe the renormalization group flow backgrounds at zero and finite temperatures, we calculate the minimum surfaces of the corresponding string worldsheets. We show that a holographic renormalization group flow at T = 0 mimicking the QCD behavior of the running coupling has a confining phase at long distances, while the renormalization group flow with an anti-de Sitter ultraviolet fixed point is nonconfining.

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. M. Maldacena, “The large N limit of superconformai field theories and supergravity,” Internat. J. Theor. Phys., 38, 1113–1133 (1999); Adv. Theor. Math. Phys., 2, 231–252 (1998); arXiv:hep-th/9711200v3 (1997).

    Article  ADS  Google Scholar 

  2. S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, “Gauge theory correlators from non-critical string theory,” Phys. Lett. B, 428, 105–114 (1998); arXiv:hep-th/9802109v2 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  3. E. Witten, “Anti de Sitter space and holography,” Adv. Theor. Math. Phys., 2, 253–291 (1998); arXiv:hep-th/9802150v2 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  4. J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal, and U. A. Wiedemann, Gauge/String Duality, Hot QCD, and Heavy Ion Collisions, Cambridge Univ. Press, Cambridge (2014); arXiv:1101.0618v2 [hep-th] (2011).

    Book  Google Scholar 

  5. I. Ya. Aref’eva, “Holographic approach to quark—gluon plasma in heavy ion collisions,” Phys. Usp., 57, 527–555 (2014).

    Article  ADS  Google Scholar 

  6. J. de Boer, E. P. Verlinde, and H. L. Verlinde, “On the holographic renormalization group,” JHEP, 0008, 003 (2000); arXiv:hep-th/9912012v1 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  7. H. J. Boonstra, K. Skenderis, and P. K. Townsend, “The domain wall/QFT correspondence,” JHEP, 9901, 003 (1999); arXiv:hep-th/9807137v2 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  8. M. Bianchi, D. Z. Freedman, and K. Skenderis, “Holographic renormalization,” Nucl. Phys. B, 631, 159–194 (2002); arXiv:hep-th/0112119v2 (2001).

    Article  ADS  MathSciNet  Google Scholar 

  9. K. Skenderis, “Lecture notes on holographic renormalization,” Class. Q. Grav., 19, 5849–5876 (2002); arXiv:hep-th/0209067v2 (2002).

    Article  MathSciNet  Google Scholar 

  10. E. T. Akhmedov, “A remark on the AdS/CFT correspondence and the renormalization group flow,” Phys. Lett. B, 442, 152–158 (1998); arXiv:hep-th/9806217v3 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  11. U. Gürsoy and E. Kiritsis, “Exploring improved holographic theories for QCD: Part I,” JHEP, 0802, 032 (2008); arXiv:0707.1324v3 [hep-th] (2007).

    Article  ADS  Google Scholar 

  12. U. Gürsoy, E. Kiritsis, and F. Nitti, “Exploring improved holographic theories for QCD: part II,” JHEP, 0802, 019 (2008); arXiv:0707.1349v3 [hep-th] (2007).

    Article  ADS  Google Scholar 

  13. M. Järvinen and E. Kiritsis, “Holographic models for QCD in the Veneziano limit,” JHEP, 1203, 002 (2012); arXiv:1112.1261v2 [hep-ph] (2011).

    Article  ADS  Google Scholar 

  14. D. Giataganas, U. Gursoy, and J. F. Pedraza, “Strongly coupled anisotropic gauge theories and holography,” Phys. Rev. Lett., 121, 121601 (2018); arXiv:1708.05691v2 [hep-th] (2017).

    Article  ADS  Google Scholar 

  15. U. Gürsoy, M. Järvinen, G. Nijs, and J. F. Pedraza, “Inverse anisotropic catalysis in holographic QCD,” JHEP, 1904, 071 (2019); arXiv:1811.11724v2 [hep-th] (2018).

    Article  ADS  MathSciNet  Google Scholar 

  16. I. Aref’eva and K. Rannu, “Holographic anisotropic background with confinement—deconfinement phase transition,” JHEP, 1805, 206 (2018); arXiv:1802.05652v3 [hep-th] (2018).

    Article  ADS  MathSciNet  Google Scholar 

  17. I. Y. Aref’eva, A. A. Golubtsova, and G. Policastro, “Exact holographic RG flows and the A1 × A1 Toda chain,” JHEP, 1905, 117 (2019); arXiv:1803.06764v2 [hep-th] (2018).

    Article  ADS  Google Scholar 

  18. U. Gürsoy, M. Järvinen, and G. Policastro, “Late time behavior of non-conformal plasmas,” JHEP, 1601, 134 (2016); arXiv:1507.08628v1 [hep-th] (2015).

    Article  ADS  MathSciNet  Google Scholar 

  19. U. Gursoy, “Continuous Hawking—Page transitions in Einstein—scalar gravity,” JHEP, 1101, 086 (2011); arXiv:1007.0500v1 [hep-th] (2010).

    Article  ADS  MathSciNet  Google Scholar 

  20. H. Lü, C. N. Pope, E. Sezgin, and K. S. Stelle, “Dilatonic p-brane solitons,” Phys. Lett. B, 371, 46–50 (1996); arXiv:hep-th/9511203v1 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  21. E. Kiritsis, W. Li, and F. Nitti, “Holographic RG flow and the quantum effective action,” Fortsch. Phys., 62, 389–454 (2014); arXiv:1401.0888v2 [hep-th] (2014).

    Article  ADS  MathSciNet  Google Scholar 

  22. J. M. Maldacena, “Wilson loops in large N field theories,” Phys.Rev.Lett., 80, 4859–4862 (1998); arXiv:hep-th/9803002v3 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  23. S.-J. Rey and J.-T. Yee, “Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter super-gravity,” Eur. Phys. J. C, 22, 379–394 (2001); arXiv:hep-th/9803001v3 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  24. S.-J. Rey, S. Theisen, and J.-T. Yee, “Wilson—Polyakov loop at finite temperature in large-N gauge theory and anti-de Sitter supergravity,” Nucl. Phys. B, 527, 171–186 (1998); arXiv:hep-th/9803135v2 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  25. A. Brandhuber, N. Itzhaki, J. Sonnenschein, and S. Yankielowicz, “Wilson loops, confinement, and phase transitions in large N gauge theories from supergravity,” JHEP, 9806, 001 (1998); arXiv:hep-th/9803263v3 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  26. J. Distler and F. Zamora, “Non-supersymmetric conformal field theories from stable anti-de Sitter spaces,” Adv. Theor. Math. Phys., 2, 1405–1439 (1999); arXiv:hep-th/9810206v3 (1998).

    Article  MathSciNet  Google Scholar 

  27. L. Girardello, M. Petrini, M. Porrati, and A. Zaffaroni, “Confinement and condensates without fine tuning in supergravity duals of gauge theories,” JHEP, 9905, 026 (1999); arXiv:hep-th/9903026v2 (1999).

    Article  ADS  Google Scholar 

  28. L. Girardello, M. Petrini, M. Porrati, and A. Zaffaroni, “The supergravity dual of N=1 super Yang—Mills theory,” Nucl. Phys. B, 569, 451–469 (2000); arXiv:hep-th/9909047v2 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  29. A. Zaffaroni, “The holographic RG flow to conformal and non-conformal theory,” PoS (TMR99), 053 (1999); arXiv:hep-th/0002172v2 (2000).

  30. I. Aref’eva, K. Rannu, and P. Slepov, “Orientation dependence of confinement—deconfinement phase transition in anisotropic media,” Phys. Lett. B, 792, 470–475 (2019); arXiv:1808.05596v3 [hep-th] (2018).

    Article  ADS  Google Scholar 

  31. J. Casalderrey-Solana, D. Gutiez, and C. Hoyos, “Effective long distance \(q\bar q\) potential in holographic RG flows,” JHEP, 1904, 134 (2019); arXiv:1902.04279v2 [hep-th] (2019).

    Article  ADS  Google Scholar 

  32. I. Aref’eva, “Holography for heavy-ion collisions at LHC and NICA: Results of the last two years,” EPJ Web Conf., 191, 05010 (2018).

    Article  Google Scholar 

  33. D. Giataganas, “Probing strongly coupled anisotropic plasma,” JHEP, 1207, 031 (2012); arXiv:1202.4436v2[hep-th] (2012).

    Article  ADS  Google Scholar 

  34. S. S. Gubser, “Curvature singularities: The good, the bad, and the naked,” Adv. Theor. Math. Phys., 4, 679–745 (2000); arXiv:hep-th/0002160v1 (2000).

    Article  MathSciNet  Google Scholar 

  35. R. E. Aria and G. A. Silva, “Wilson loops stability in the gauge/string correspondence,” JHEP, 1001, 023 (2010); arXiv:0911.0662v3 [hep-th] (2009).

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgments

The authors thank I. Ya. Aref’eva, G. Policastro, K. Rannu, and P. Slepov for the helpful discussions and comments.

Author information

Authors and Affiliations

  1. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia

    A. A. Golubtsova & V. H. Nguyen

  2. Dubna State University, Dubna, Moscow Oblast, Russia

    A. A. Golubtsova

  3. Institute of Physics, Vietnamese Academy of Science and Technology, Hanoi, Vietnam

    V. H. Nguyen

Authors
  1. A. A. Golubtsova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. H. Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to A. A. Golubtsova or V. H. Nguyen.

Additional information

The research of A. A. Golubtsova is supported by the Russian Foundation for Basic Research (Research Project No. 18-02-40069 mega).

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 202, No. 2, pp. 243–263, February, 2020.

Conflicts of interest

The authors declare no conflicts of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Golubtsova, A.A., Nguyen, V.H. Wilson Loops in Exact Holographic RG Flows at Zero and Finite Temperatures. Theor Math Phys 202, 214–230 (2020). https://doi.org/10.1134/S0040577920020051

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0040577920020051

Keywords

Search

Navigation