Holographic and Wilsonian renormalization groups

We develop parallels between the holographic renormalization group in the bulk and the Wilsonian renormalization group in the dual field theory. Our philosophy differs from most previous work on the holographic RG; the most notable feature is the key role of multi-trace operators. We work out the forms of various single-and double-trace flows. The key question, ‘what cutoff on the field theory corresponds to a radial cutoff in the bulk?’ is left unanswered, but by sharpening the analogy between the two sides we identify possible directions.

[1]  Perturbative search for fixed lines in large-N gauge theories , 2005, hep-th/0505099.

[2]  Perturbative gauge theory and closed string tachyons , 2005, hep-th/0509132.

[3]  Susskind,et al.  The stretched horizon and black hole complementarity. , 1993, Physical review. D, Particles and fields.

[4]  Multiple-Trace Operators and Non-Local String Theories , 2001, hep-th/0105309.

[5]  Ads/CFT correspondence and symmetry breaking , 1999, hep-th/9905104.

[6]  Irene Bredberg,et al.  Wilsonian approach to fluid/gravity duality , 2010, 1006.1902.

[7]  H. Murayama,et al.  Holomorphy, Rescaling Anomalies and Exact $\beta$ Functions in Supersymmetric Gauge Theories , 1997, hep-th/9707133.

[8]  G. Horowitz,et al.  Towards a Big Crunch Dual , 2004, hep-th/0406134.

[9]  E. Akhmedov.  A remark on the AdS/CFT correspondence and the renormalization group flow , 1998 .

[10]  Hong Liu,et al.  Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm , 2008, 0809.3808.

[11]  K. Wilson.  The renormalization group and critical phenomena , 1983 .

[12]  L. Girardello,et al.  Novel Local CFT and Exact Results on Perturbations of N=4 Super Yang Mills from AdS Dynamics , 1998, hep-th/9810126.

[13]  W. Mueck.  Spectral functions in holographic renormalization group flows , 2008, 0811.2072.

[14]  J. Polchinski,et al.  Semi-holographic Fermi liquids , 2010, 1001.5049.

[15]  A Note on Multi-trace Deformations and AdS/CFT , 2002, hep-th/0203168.

[16]  Holographic representation of local bulk operators , 2006, hep-th/0606141.

[17]  An improved correspondence formula for AdS/CFT with multi-trace operators , 2002, hep-th/0201100.

[18]  Holography and renormalization in Lorentzian signature , 2006, hep-th/0606022.

[19]  A. Sever,et al.  `Double-trace' deformations, boundary conditions and spacetime singularities , 2001, hep-th/0112264.

[20]  A manifestly gauge invariant exact renormalization group , 1998, hep-th/0606181.

[21]  J. de Boer,et al.  On the holographic renormalization group , 1999 .

[22]  Construction of local fields in the bulk of AdS 5 and other spaces , 1999, hep-th/9905186.

[23]  RG-flow, gravity and the cosmological constant , 1999, hep-th/9912018.

[24]  Holographic Probes of Anti-de Sitter Spacetimes , 1998, hep-th/9808017.

[25]  Multitrace operators and the generalized AdS/CFT prescription , 2002, hep-th/0201172.

[26]  E. Musaev,et al.  Exact statement for Wilsonian and holographic renormalization group , 2010, 1001.4067.

[27]  The Wilson–Polchinski renormalization group equation in the planar limit , 2002, hep-th/0202155.

[28]  L. Susskind,et al.  The Holographic bound in anti-de Sitter space , 1998, hep-th/9805114.

[29]  R. Brustein,et al.  Renormalization group equation and non-perturbative effects in string-field theory , 1991 .

[30]  E. Witten.  Anti-de Sitter space and holography , 1998, hep-th/9802150.

[31]  T. Faulkner,et al.  Integrating out geometry: holographic Wilsonian RG and the membrane paradigm , 2010, 1010.4036.

[32]  AdS/CFT correspondence and geometry , 2004, hep-th/0404176.

[33]  D. Simmons-Duffin,et al.  Effective conformal theory and the flat-space limit of AdS , 2010, 1007.2412.

[34]  D. Son,et al.  Deconstructing holographic liquids , 2010, 1009.3094.

[35]  T. Faulkner,et al.  New stability results for Einstein scalar gravity , 2010, 1006.2387.

[36]  Geometric holography, the renormalization group and the c theorem , 1998, hep-th/9807226.

[37]  J. Wheeler.  SUPERSPACE AND THE NATURE OF QUANTUM GEOMETRODYNAMICS. , 1968 .

[38]  Joseph Polchinski,et al.  Renormalization and effective lagrangians , 1984 .

[39]  AdS Dynamics from Conformal Field Theory , 1998, hep-th/9808016.

[40]  L. Rastelli,et al.  Large N field theory and AdS tachyons , 2008, 0805.2261.

[41]  S. Hawking,et al.  Path Integrals and the Indefiniteness of the Gravitational Action , 1978 .

[42]  Multi-Trace Operators, Boundary Conditions, And AdS/CFT Correspondence , 2001, hep-th/0112258.

[43]  R. Bousso.  Preprint typeset in JHEP style-HYPER VERSION Complementarity in the Multiverse , 2009 .

[44]  M. Porrati,et al.  RG fixed points in supergravity duals of 4-d field theory and asymptotically AdS spaces , 1999, hep-th/9903085.

[45]  A. Polyakov,et al.  Gauge Theory Correlators from Non-Critical String Theory , 1998, hep-th/9802109.

[46]  Non-supersymmetric conformal field theories from stable anti-de Sitter spaces , 1998, hep-th/9810206.

[47]  Kostas Skenderis.  Lecture notes on holographic renormalization , 2002 .

[48]  Closed string tachyons, AdS / CFT, and large N QCD , 2001, hep-th/0103220.

[49]  J. Maldacena.  The Large-N Limit of Superconformal Field Theories and Supergravity , 1997, hep-th/9711200.

[50]  SPACETIME AND THE HOLOGRAPHIC RENORMALIZATION GROUP , 1999, hep-th/9903190.

[51]  Sung-Sik Lee.  Holographic description of quantum field theory , 2009, 0912.5223.

[52]  B. Dewitt.  Quantum Theory of Gravity. I. The Canonical Theory , 1967 .

[53]  T. Faulkner,et al.  Holographic quantum criticality from multi-trace deformations , 2010, 1008.1581.

[54]  J. Trampetić,et al.  Moments of inertia, nucleon axial-vector coupling, the {\bf 8}, {\bf 10}, $\bar{\bf 10}$ and ${\bf 27}_{3/2}$ mass spectrums and the higher SU(3)_f representation mass splittings in the Skyrme model , 2004 .

[55]  S. Gubser,et al.  Renormalization group flows from holography supersymmetry and a c theorem , 1999, hep-th/9904017.

[56]  L. Vecchi.  Multitrace deformations, Gamow states, and stability of AdS/CFT , 2010, 1005.4921.

[57]  J. Polchinski,et al.  Holography from Conformal Field Theory , 2009, 0907.0151.

[58]  E. Witten,et al.  Superconformal field theory on threebranes at a Calabi-Yau singularity , 1998, hep-th/9807080.

[59]  S. Hawking,et al.  Action Integrals and Partition Functions in Quantum Gravity , 1977 .

[60]  J. Sully,et al.  More holography from conformal field theory , 2010, 1006.0976.

[61]  A Note on relation between holographic RG equation and Polchinski's RG equation , 2000, hep-th/0001193.

[62]  A. Petkou.  Boundary multi-trace deformations and OPEs in AdS/CFT correspondence , 2002, hep-th/0201258.

[63]  The holographic Weyl anomaly , 1998, hep-th/9806087.