Holographic and Wilsonian renormalization groups

By Idse Heemskerk, J. Polchinski. 2010

427 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b56bbb49f7b3b6c6cd68b1f0d6456ae3cf2242f9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. D. Harlow
2. T. Takayanagi
3. S. Hartnoll
4. S. Sachdev
5. R. Myers
6. D. Stanford
7. V. Hubeny
8. J. Polchinski

In Nuclear and High Energy Physics

1. D. Harlow
2. T. Takayanagi
3. Thomas Hartman
4. S. Hartnoll
5. R. Myers
6. V. Hubeny
7. S. Raju
8. D. Stanford

Citations in the corpus

• Analyticity and the holographic S-matrix (2011, background): “Locality is one of the most important ideas in physics, and understanding it [16, 17, 18, 19, 38] has only become more urgent since the discovery that a local spacetime can emerge holographically from a lower dimensional theory, as in the AdS/CFT correspondence [6, 7, 8].”
• Holographic Quantum Matter (2016, methodology): “Using standard manipulations of Hamiltonian mechanics, with the radial direction playing the role of time [256; 365], from (48) one can obtain the (Legendre transformed) Hamilton-Jacobi functional equation √ grr∂ IΛ[O] = (50) ∫ dx √−γ ( 1”
• Bulk and transhorizon measurements in AdS/CFT (2012, positive): “The holographic analog of the Wilsonian renormalization group [49, 50] suggests a framework for this.”
• Holographic geometry of entanglement renormalization in quantum field theories (2012, methodology): “) Though traditionally the extra dimension of a AdS has often been identified with the energy scale of the Wilsonian renormalization group flow in momentum space [30, 31, 32], the calculation of the entanglement entropy suggests that AdS/CFT fits nicely with the real space renormalization group sche”
• Aspects of holography for theories with hyperscaling violation (2012, background): “This has been put on a firmer footing for asymptotically AdS spacetimes in [36].”
• Light-front holographic QCD and emerging confinement (2014, background): “Of particular interest is the formulation of holographic renormalization flows for strongly interacting theories with a cut-off in the bulk, where integration of high energy modes corresponds to integrate the bulk geometry up to some intermediate scale to extract the low-energy effective theory of t”
• Moving the CFT into the bulk with TT¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ T\overline{T} $$\end{document} (2016, background): “In the formulation of [8] (see also [9–12]) the CFT partition sum ZCFT is identified with the gravity partition function in which the bulk path integral is cut into an IR and UV part via”
• TT deformations in general dimensions (2018, neutral): “In [14, 15], it was proposed that the holographic dual at finite radius should be interpreted as a deformed CFT.”
• Integrating out geometry: holographic Wilsonian RG and the membrane paradigm (2010, background): “10 The expressions below were obtained earlier [25] and in [23] in the pure AdS limit.”
• Lectures on holographic non-Fermi liquids and quantum phase transitions (2011, background): “62) can also be derived directly following the formalism of holographic Wilsonian RG introduced recently in [81, 82].”
• Holography at finite cutoff with a T2 deformation (2018, result): “a boundary EFT that can be studied on its own terms. This is the perspective taken in [8], in contrast to the earlier work cited above. This approach leaves open the mysterious question emphasized in [4,35] of what coarse-graining or cutoff procedure in the QFT actually produces the flow (1.1). If thi”
• TASI Lectures on the Emergence of Bulk Physics in AdS/CFT (2017, background): “Since these ideas use many aspects of AdS/CFT, I will present the correspondence more or less from the beginning.”