Abstract
We propose a local renormalization group procedure where length scale is changed in spacetime dependent way. Combining this scheme with an earlier observation that high energy modes in renormalization group play the role of dynamical sources for low energy modes at each scale, we provide a prescription to derive background independent holographic duals for field theories. From a first principle construction, it is shown that the holographic theory dual to a D-dimensional matrix field theory is a (D + 1)-dimensional quantum theory of gravity coupled with matter fields of various spins. The gravitational theory has (D + 1) first-class constraints which generate local spacetime transformations in the bulk. The (D + 1)-dimensional diffeomorphism invariance is a consequence of the freedom to choose different local RG schemes.
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References
J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
E.T. Akhmedov, Notes on multitrace operators and holographic renormalization group, hep-th/0202055 [INSPIRE].
S.R. Das and A. Jevicki, Large-N collective fields and holography, Phys. Rev. D 68 (2003) 044011 [hep-th/0304093] [INSPIRE].
R. Gopakumar, From free fields to AdS, Phys. Rev. D 70 (2004) 025009 [hep-th/0308184] [INSPIRE].
R. Gopakumar, From free fields to AdS. 2., Phys. Rev. D 70 (2004) 025010 [hep-th/0402063] [INSPIRE].
I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from Conformal Field Theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [INSPIRE].
S.-S. Lee, Holographic description of quantum field theory, Nucl. Phys. B 832 (2010) 567 [arXiv:0912.5223] [INSPIRE].
R. de Mello Koch, A. Jevicki, K. Jin and J.P. Rodrigues, AdS 4 /CF T 3 Construction from Collective Fields, Phys. Rev. D 83 (2011) 025006 [arXiv:1008.0633] [INSPIRE].
I. Heemskerk and J. Polchinski, Holographic and Wilsonian Renormalization Groups, JHEP 06 (2011) 031 [arXiv:1010.1264] [INSPIRE].
T. Faulkner, H. Liu and M. Rangamani, Integrating out geometry: Holographic Wilsonian RG and the membrane paradigm, JHEP 08 (2011) 051 [arXiv:1010.4036] [INSPIRE].
M.R. Douglas, L. Mazzucato and S.S. Razamat, Holographic dual of free field theory, Phys. Rev. D 83 (2011) 071701 [arXiv:1011.4926] [INSPIRE].
R. Sundrum, From Fixed Points to the Fifth Dimension, arXiv:1106.4501 [INSPIRE].
S.-S. Lee, Holographic description of large-N gauge theory, Nucl. Phys. B 851 (2011) 143 [arXiv:1011.1474] [INSPIRE].
D. Radicevic, Connecting the Holographic and Wilsonian Renormalization Groups, JHEP 12 (2011) 023 [arXiv:1105.5825] [INSPIRE].
S.-S. Lee, Holographic Matter: Deconfined String at Criticality, Nucl. Phys. B 862 (2012) 781 [arXiv:1108.2253] [INSPIRE].
J. de Boer, E.P. Verlinde and H.L. Verlinde, On the holographic renormalization group, JHEP 08 (2000) 003 [hep-th/9912012] [INSPIRE].
M. Li, A Note on relation between holographic RG equation and Polchinski’s RG equation, Nucl. Phys. B 579 (2000) 525 [hep-th/0001193] [INSPIRE].
X.-G. Wen, Quantum orders and symmetric spin liquids, Phys. Rev. B 65 (2002) 165113 [INSPIRE].
A. Sakharov, Vacuum quantum fluctuations in curved space and the theory of gravitation, Sov. Phys. Dokl. 12 (1968) 1040 [INSPIRE].
J. Polchinski, Renormalization and Effective Lagrangians, Nucl. Phys. B 231 (1984) 269 [INSPIRE].
J. Polonyi, Lectures on the functional renormalization group method, Central Eur. J. Phys. 1 (2003) 1 [hep-th/0110026] [INSPIRE].
R.L. Arnowitt, S. Deser and C.W. Misner, Dynamical Structure and Definition of Energy in General Relativity, Phys. Rev. 116 (1959) 1322 [INSPIRE].
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ArXiv ePrint: 1204.1780
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Lee, SS. Background independent holographic description: from matrix field theory to quantum gravity. J. High Energ. Phys. 2012, 160 (2012). https://doi.org/10.1007/JHEP10(2012)160
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DOI: https://doi.org/10.1007/JHEP10(2012)160