Journal of Holography Applications in Physics
Holographic RG flow triggered by gluon condensate
Document Type : Regular article
Author
Department of Physics and Photon Science, Gwangju Institute of Science and Technology, Gwangju 61005, Korea
Abstract
By applying the holographic method, we study a non-perturbative renormalization group (RG) flow triggered by a gluon condensate. After introducing a bulk scalar field in an AdS space related to the gluon condensate, we investigate the trace anomaly proportional to the gluon condensate. The holographic calculation reproduces the one-loop trace anomaly known in the lattice QCD. We also show that higher loop corrections give rise to additional contributions and modify the one-loop trace anomaly.
Keywords
Main Subjects
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[2] S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “Gauge theory correlators from noncritical string theory,” Phys. Lett. B 428, 105-114 (1998) [arXiv:hep-th/9802109 [hep-th]].
[3] E. Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys. 2, 253-291 (1998) [arXiv:hep-th/9802150 [hep-th]].
[4] E. Witten, “Anti-de Sitter space, thermal phase transition, and confinement in gauge theories,” Adv. Theor. Math. Phys. 2, 505-532 (1998) [arXiv:hep-th/9803131 [hep-th]].
[5] M. Henningson and K. Skenderis, “The Holographic Weyl anomaly,” JHEP 07, 023 (1998) [arXiv:hep-th/9806087 [hep-th]].
[6] M. Henningson and K. Skenderis, “Holography and the Weyl anomaly,” Fortsch. Phys. 48, 125-128 (2000) [arXiv:hep-th/9812032 [hep-th]].
[7] D. Z. Freedman, S. D. Mathur, A. Matusis and L. Rastelli, “Correlation functions in the CFT(d) / AdS(d+1) correspondence,” Nucl. Phys. B 546, 96-118 (1999) [arXiv:hep- th/9804058 [hep-th]].
[8] S. S. Gubser, “AdS / CFT and gravity,” Phys. Rev. D 63, 084017 (2001) [arXiv:hep-th/9912001 [hep-th]].
[9] J. de Boer, E. P. Verlinde and H. L. Verlinde, “On the holographic renormalization group,” JHEP 08, 003 (2000) [arXiv:hep-th/9912012 [hep-th]].
[10] E. P. Verlinde and H. L. Verlinde, “RG flow, gravity and the cosmological constant,” JHEP 05, 034 (2000) [arXiv:hep-th/9912018 [hep-th]].
[11] J. de Boer, “The Holographic renormalization group,” Fortsch. Phys. 49, 339-358 (2001) [arXiv:hep-th/0101026 [hep-th]].
[12] K. Skenderis and P. K. Townsend, “Gravitational stability and renormalization group flow,” Phys. Lett. B 468, 46-51 (1999) [arXiv:hep-th/9909070 [hep-th]].
[13] J. Polchinski and J. Sully, “Wilson Loop Renormalization Group Flows,” JHEP 10, 059 (2011) [arXiv:1104.5077 [hep-th]].
[14] I. Papadimitriou, “Holographic renormalization as a canonical transformation,” JHEP 11, 014 (2010) [arXiv:1007.4592 [hep-th]].
[15] I. Papadimitriou and K. Skenderis, “AdS / CFT correspondence and geometry,” IRMA Lect. Math. Theor. Phys. 8, 73-101 (2005) [arXiv:hep-th/0404176 [hep-th]].
[16] K. Skenderis, “Lecture notes on holographic renormalization,” Class. Quant. Grav. 19, 5849-5876 (2002) [arXiv:hep-th/0209067 [hep-th]].
[17] I. Heemskerk and J. Polchinski, “Holographic and Wilsonian Renormalization Groups,” JHEP 06, 031 (2011) [arXiv:1010.1264 [hep-th]].
[18] J. Erdmenger, C. M. Melby-Thompson and C. Northe, “Holographic RG Flows for Kondo-like Impurities,” JHEP 05, 075 (2020) [arXiv:2001.04991 [hep-th]].
[19] C. Northe, “Review on Top-Down Kondo-like Holographic RG Flows,” Journal of Holography Applications in Physics 2, (3), 1-54 (2022).
[20] K. S. Kim and C. Park, “Renormalization group flow of entanglement entropy to thermal entropy,” Phys. Rev. D 95, no.10, 106007 (2017) [arXiv:1610.07266 [hep-th]].
[21] C. Park, D. Ro and J. Hun Lee, “c-theorem of the entanglement entropy,” JHEP 11, 165 (2018) [arXiv:1806.09072 [hep-th]].
[22] C. Park and J. Hun Lee, “Exotic RG flow of entanglement entropy,” Phys. Rev. D 101, no.8, 086008 (2020) [arXiv:1910.05741 [hep-th]].
[23] C. Park and J. H. Lee, “Holographic renormalization group flow effect on quantum correlations,” JHEP 02, 135 (2021) [arXiv:2008.04507 [hep-th]].
[24] C. Park, “Holographic two-point functions in a disorder system,” [arXiv:2209.07721 [hep-th]].
[25] A. Di Giacomo and G. Rossi, “Extracting 〈(α/π)Σa,μν Gμν aGμν a〉 from gauge theories on a lattice,” Phys. Lett. B 100, 481 (1981).
[26] R. C. Trinchero, “Pure gauge QCD and holography,” Int. J. Mod. Phys. A 29, no.24, 1450131 (2014) [arXiv:1310.5913 [hep-ph]].
[27] C. Park, “Holographic RG flow triggered by a classically marginal operator,” Phys. Rev. D 105, no.4, 046004 (2022) [arXiv:2102.01829 [hep-th]].
[28] T. J. Hollowood, “6 Lectures on QFT, RG and SUSY,” [arXiv:0909.0859 [hep-th]].
[29] Y. Kim, B. H. Lee, C. Park and S. J. Sin, “Gluon Condensation at Finite Temperature via AdS/CFT,” JHEP 09, 105 (2007) [arXiv:hep-th/0702131 [hep-th]].
[30] Y. Kim, B. H. Lee, C. Park and S. J. Sin, “The Effect of gluon condensate on holographic heavy quark potential,” Phys. Rev. D 80, 105016 (2009) [arXiv:0808.1143 [hep-th]].
[31] Y. Ko, B. H. Lee and C. Park, “Meson spectra in a gluon condensate background,” JHEP 04, 037 (2010) [arXiv:0912.5274 [hep-ph]].
[32] D. Friedan, “Nonlinear Models in 2 + Dimensions,” Phys. Rev. Lett. 45, 1057 (1980). [33] D. H. Friedan, “Nonlinear models in 2 + dimensions,” Annals of Physics 163, 318 (1985).
[34] D. Z. Freedman, S. S. Gubser, K. Pilch and N. P. Warner, “Renormalization group flows from holography supersymmetry and a c theorem,” Adv. Theor. Math. Phys. 3, 363-417 (1999) [arXiv:hep-th/9904017 [hep-th]].
[35] O. DeWolfe, D. Z. Freedman, S. S. Gubser and A. Karch, “Modeling the fifth-dimension with scalars and gravity,” Phys. Rev. D 62, 046008 (2000) [arXiv:hep-th/9909134 [hep-th]].
[36] C. Csaki, J. Erlich, C. Grojean and T. J. Hollowood, “General properties of the self- tuning domain wall approach to the cosmological constant problem,” Nucl. Phys. B 584, 359-386 (2000) [arXiv:hep-th/0004133 [hep-th]].
[37] S. S. Gubser, “Dilaton driven confinement,” [arXiv:hep-th/9902155 [hep-th]].
[38] A. Kehagias and K. Sfetsos, “On Running couplings in gauge theories from type IIB supergravity,” Phys. Lett. B 454, 270-276 (1999) [arXiv:hep-th/9902125 [hep-th]].
[39] C. Csaki and M. Reece, “Toward a systematic holographic QCD: A Braneless approach,” JHEP 05, 062 (2007) [arXiv:hep-ph/0608266 [hep-ph]].
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Volume 3, Issue 2
June 2023Pages 41-52
- Receive Date: 20 April 2023
- Revise Date: 20 May 2023
- Accept Date: 24 May 2023