Abstract
The bulk locality in the constructive holographic renormalization group requires miraculous cancellations among various local renormalization group functions. The cancellation is not only from the properties of the spectrum but from more detailed aspects of operator product expansions in relation to conformal anomaly. It is remarkable that one-loop computation of the universal local renormalization group functions in the weakly coupled limit of the \( \mathcal{N}=4 \) super Yang-Mills theory fulfils the necessary condition for the cancellation in the strongly coupled limit in its SL(2, Z) duality invariant form. From the consistency between the quantum renormalization group and the holographic renormalization group, we determine some unexplored local renormalization group functions (e.g. diffusive term in the beta function for the gauge coupling constant) in the strongly coupled limit of the planar \( \mathcal{N}=4 \) super Yang-Mills theory.
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References
I. Heemskerk and J. Polchinski, Holographic and Wilsonian renormalization groups, JHEP 06 (2011) 031 [arXiv:1010.1264] [INSPIRE].
S.-S. Lee, Holographic description of large-N gauge theory, Nucl. Phys. B 851 (2011) 143 [arXiv:1011.1474] [INSPIRE].
S.-S. Lee, Background independent holographic description: from matrix field theory to quantum gravity, JHEP 10 (2012) 160 [arXiv:1204.1780] [INSPIRE].
S.-S. Lee, Quantum renormalization group and holography, JHEP 01 (2014) 076 [arXiv:1305.3908] [INSPIRE].
E. Mintun and J. Polchinski, Higher Spin Holography, RG and the Light Cone, arXiv:1411.3151 [INSPIRE].
P. Lunts et al., Ab Initio Holography, arXiv:1503.06474 [INSPIRE].
N. Behr, S. Kuperstein and A. Mukhopadhyay, Holography as a highly efficient RG flow. Part 1, arXiv:1502.06619 [INSPIRE].
S. El-Showk and K. Papadodimas, Emergent spacetime and holographic CFTs, JHEP 10 (2012) 106 [arXiv:1101.4163] [INSPIRE].
Y. Nakayama, a − c test of holography versus quantum renormalization group, Mod. Phys. Lett. A 29 (2014) 1450158 [arXiv:1401.5257] [INSPIRE].
S. Jackson, R. Pourhasan and H. Verlinde, Geometric RG flow, arXiv:1312.6914 [INSPIRE].
E. Kiritsis, W. Li and F. Nitti, Holographic RG flow and the Quantum Effective Action, Fortsch. Phys. 62 (2014) 389 [arXiv:1401.0888] [INSPIRE].
I.L. Buchbinder, N.G. Pletnev and A.A. Tseytlin, ’Induced’ N = 4 conformal supergravity, Phys. Lett. B 717 (2012) 274 [arXiv:1209.0416] [INSPIRE].
H. Osborn, Local couplings and \( \mathrm{S}\mathrm{L}\left(2,\;\mathbb{R}\right) \) invariance for gauge theories at one loop, Phys. Lett. B 561 (2003) 174 [hep-th/0302119] [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, Asymptotic freedom in extended conformal supergravities, Phys. Lett. B 110 (1982) 117 [INSPIRE].
H. Osborn, Weyl consistency conditions and a local renormalization group equation for general renormalizable field theories, Nucl. Phys. B 363 (1991) 486 [INSPIRE].
Y. Nakayama, Scale invariance vs conformal invariance, Phys. Rept. 569 (2015) 1 [arXiv:1302.0884] [INSPIRE].
Y. Nakayama, Consistency of local renormalization group in d = 3, Nucl. Phys. B 879 (2014) 37 [arXiv:1307.8048] [INSPIRE].
I. Jack and H. Osborn, Constraints on RG Flow for Four Dimensional Quantum Field Theories, Nucl. Phys. B 883 (2014) 425 [arXiv:1312.0428] [INSPIRE].
F. Baume, B. Keren-Zur, R. Rattazzi and L. Vitale, The local Callan-Symanzik equation: structure and applications, JHEP 08 (2014) 152 [arXiv:1401.5983] [INSPIRE].
R. Auzzi and B. Keren-Zur, Superspace formulation of the local RG equation, JHEP 05 (2015) 150 [arXiv:1502.05962] [INSPIRE].
D.V. Fursaev, Black hole thermodynamics, induced gravity and gravity in brane worlds, hep-th/0009164 [INSPIRE].
S.N. Solodukhin, Newton constant, contact terms and entropy, Phys. Rev. D 91 (2015) 084028 [arXiv:1502.03758] [INSPIRE].
H. Liu and A.A. Tseytlin, D = 4 super Yang-Mills, D = 5 gauged supergravity and D = 4 conformal supergravity, Nucl. Phys. B 533 (1998) 88 [hep-th/9804083] [INSPIRE].
P. Hořava, Membranes at quantum criticality, JHEP 03 (2009) 020 [arXiv:0812.4287] [INSPIRE].
P. Hořava, Quantum Gravity at a Lifshitz Point, Phys. Rev. D 79 (2009) 084008 [arXiv:0901.3775] [INSPIRE].
T. Griffin, P. Hořava and C.M. Melby-Thompson, Conformal Lifshitz gravity from holography, JHEP 05 (2012) 010 [arXiv:1112.5660] [INSPIRE].
T. Griffin, P. Hořava and C.M. Melby-Thompson, Lifshitz Gravity for Lifshitz Holography, Phys. Rev. Lett. 110 (2013) 081602 [arXiv:1211.4872] [INSPIRE].
D. Blas, O. Pujolàs and S. Sibiryakov, On the extra mode and inconsistency of Hořava gravity, JHEP 10 (2009) 029 [arXiv:0906.3046] [INSPIRE].
M. Henneaux, A. Kleinschmidt and G. Lucena Gómez, A dynamical inconsistency of Hořava gravity, Phys. Rev. D 81 (2010) 064002 [arXiv:0912.0399] [INSPIRE].
M.B. Green, Interconnections between type-II superstrings, M-theory and N = 4 supersymmetric Yang-Mills, Lect. Notes Phys. 525 (1999) 22 [hep-th/9903124] [INSPIRE].
Y. Nakayama, Holographic Renormalization of Foliation Preserving Gravity and Trace Anomaly, Gen. Rel. Grav. 44 (2012) 2873 [arXiv:1203.1068] [INSPIRE].
E.P. Verlinde and H.L. Verlinde, RG flow, gravity and the cosmological constant, JHEP 05 (2000) 034 [hep-th/9912018] [INSPIRE].
M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
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Nakayama, Y. Local renormalization group functions from quantum renormalization group and holographic bulk locality. J. High Energ. Phys. 2015, 92 (2015). https://doi.org/10.1007/JHEP06(2015)092
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DOI: https://doi.org/10.1007/JHEP06(2015)092