On the gluonic operator effective potential in holographic Yang-Mills theory

Open Access
Regular Article - Theoretical Physics

Abstract

The holographic formalism is applied to the calculation of the effective potential for the scalar glueball operator. Three different versions of this operator are defined, and for each we compute the associated effective potential and discuss its properties and scheme ambiguities. For one of them, the trace of the stress tensor, the potential is fixed by scale covariance and the conformal anomaly. Contact is made to earlier attempts to guess this effective potential from the conformal anomaly. We apply our results to the Improved Holographic QCD model calculating the glueball condensate.

Keywords

Gauge-gravity correspondence Nonperturbative Effects Renormalization Group QCD 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    U. Gürsoy and E. Kiritsis, Exploring improved holographic theories for QCD: Part I, JHEP 02 (2008) 032 [arXiv:0707.1324] [INSPIRE].CrossRefGoogle Scholar
  2. [2]
    U. Gürsoy, E. Kiritsis and F. Nitti, Exploring improved holographic theories for QCD: Part II, JHEP 02 (2008) 019 [arXiv:0707.1349] [INSPIRE].CrossRefGoogle Scholar
  3. [3]
    S.S. Gubser and A. Nellore, Mimicking the QCD equation of state with a dual black hole, Phys. Rev. D 78 (2008) 086007 [arXiv:0804.0434] [INSPIRE].ADSGoogle Scholar
  4. [4]
    U. Gürsoy, E. Kiritsis, L. Mazzanti and F. Nitti, Holography and Thermodynamics of 5D Dilaton-gravity, JHEP 05 (2009) 033 [arXiv:0812.0792] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  5. [5]
    U. Gürsoy, E. Kiritsis, L. Mazzanti and F. Nitti, Improved Holographic Yang-Mills at Finite Temperature: Comparison with Data, Nucl. Phys. B 820 (2009) 148 [arXiv:0903.2859] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    E. Kiritsis, Dissecting the string theory dual of QCD, Fortsch. Phys. 57 (2009) 396 [arXiv:0901.1772] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    U. Gürsoy, E. Kiritsis, L. Mazzanti, G. Michalogiorgakis and F. Nitti, Improved Holographic QCD, Lect. Notes Phys. 828 (2011) 79 [arXiv:1006.5461] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  8. [8]
    E. Kiritsis, W. Li and F. Nitti, Holographic RG flow and the Quantum Effective Action, Fortsch. Phys. 62 (2014) 389 [arXiv:1401.0888] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, QCD and Resonance Physics. Sum Rules, Nucl. Phys. B 147 (1979) 385 [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    A. Di Giacomo and G.C. Rossi, Extracting 〈(α/π)∑a,μν G μν a G μν afrom Gauge Theories on a Lattice, Phys. Lett. B 100 (1981) 481 [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    T. Banks, R. Horsley, H.R. Rubinstein and U. Wolff, Estimate of the Gluon Condensate From Monte Carlo Calculations, Nucl. Phys. B 190 (1981) 692 [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    M. Campostrini, A. Di Giacomo and Y. Gunduc, Gluon Condensation in SU(3) Lattice Gauge Theory, Phys. Lett. B 225 (1989) 393 [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    G. Boyd and D.E. Miller, The Temperature dependence of the SU(N c) gluon condensate from lattice gauge theory, hep-ph/9608482 [INSPIRE].
  14. [14]
    D.E. Miller, The Gluon condensate in QCD at finite temperature, Acta Phys. Polon. B 28 (1997) 2937 [hep-ph/9807304] [INSPIRE].Google Scholar
  15. [15]
    G. Veneziano and S. Yankielowicz, An Effective Lagrangian for the Pure N = 1 Supersymmetric Yang-Mills Theory, Phys. Lett. B 113 (1982) 231 [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    D. Baumann and D. Green, Desensitizing Inflation from the Planck Scale, JHEP 09 (2010) 057 [arXiv:1004.3801] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  17. [17]
    D. Elander, A.F. Faedo, C. Hoyos, D. Mateos and M. Piai, Multiscale confining dynamics from holographic RG flows, JHEP 05 (2014) 003 [arXiv:1312.7160] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    E. Megias and O. Pujolàs, Naturally light dilatons from nearly marginal deformations, JHEP 08 (2014) 081 [arXiv:1401.4998] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    S.S. Gubser, Curvature singularities: The Good, the bad and the naked, Adv. Theor. Math. Phys. 4 (2000) 679 [hep-th/0002160] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  20. [20]
    E. Kiritsis and F. Nitti, On massless 4D gravitons from asymptotically AdS 5 space-times, Nucl. Phys. B 772 (2007) 67 [hep-th/0611344] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  21. [21]
    I. Papadimitriou, Holographic Renormalization of general dilaton-axion gravity, JHEP 08 (2011) 119 [arXiv:1106.4826] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  22. [22]
    M. Bianchi, D.Z. Freedman and K. Skenderis, How to go with an RG flow, JHEP 08 (2001) 041 [hep-th/0105276] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  23. [23]
    M. Bianchi, D.Z. Freedman and K. Skenderis, Holographic renormalization, Nucl. Phys. B 631 (2002) 159 [hep-th/0112119] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  24. [24]
    E. Kiritsis and V. Niarchos, The holographic quantum effective potential at finite temperature and density, JHEP 08 (2012) 164 [arXiv:1205.6205] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    J. Schechter, Effective Lagrangian with Two Color Singlet Gluon Fields, Phys. Rev. D 21 (1980) 3393 [INSPIRE].ADSGoogle Scholar
  26. [26]
    C.J. Morningstar and M.J. Peardon, The Glueball spectrum from an anisotropic lattice study, Phys. Rev. D 60 (1999) 034509 [hep-lat/9901004] [INSPIRE].ADSGoogle Scholar
  27. [27]
    Y. Chen et al., Glueball spectrum and matrix elements on anisotropic lattices, Phys. Rev. D 73 (2006) 014516 [hep-lat/0510074] [INSPIRE].ADSGoogle Scholar
  28. [28]
    I. Iatrakis, E. Kiritsis and A. Paredes, An AdS/QCD model from tachyon condensation: II, JHEP 11 (2010) 123 [arXiv:1010.1364] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    L. Del Debbio and R. Zwicky, Renormalisation group, trace anomaly and Feynman-Hellmann theorem, Phys. Lett. B 734 (2014) 107 [arXiv:1306.4274] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Crete Center for Theoretical Physics, Department of PhysicsUniversity of CreteHeraklionGreece
  2. 2.APC, Université Paris 7, CNRS/IN2P3, CEA/IRFU, Obs. de Paris, Sorbonne Paris Cité, 10Paris Cedex 13France

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