Integrating out geometry: holographic Wilsonian RG and the membrane paradigm

By T. Faulkner, Hong Liu, M. Rangamani. 2010

349 citations recorded by the source corpus.

We formulate a holographic Wilsonian renormalization group flow for strongly coupled systems with a gravity dual, motivated by the need to extract efficiently low energy behavior of such systems. Starting with field theories defined on a cut-off surface in a bulk spacetime, we propose that integrating out high energy modes in the field theory should correspond to integrating out a part of the bulk geometry. We describe how to carry out this procedure in practice in the classical gravity approximation using examples of scalar and vector fields. By integrating out bulk degrees of freedom all the way to a black hole horizon, this formulation defines a refined version of the black hole membrane paradigm. Furthermore, it also provides a derivation of the semi-holographic description of low energy physics.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/34e78e0d40a9243eacfd1b64b207c6604e30eb41

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Citations in the corpus

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”
The Shear Viscosity to Entropy Ratio: A Status Report (2011, background): “It might be interesting to ask whether the type of flow described above can be understood more systematically in the framework of the recent attempts to refine notions of holographic RG flow [83–86], especially in the constructions of [84, 86].”
Aspects of holography for theories with hyperscaling violation (2012, background): “This has been put on a firmer footing for asymptotically AdS spacetimes in [23].”
Holography at finite cutoff with a T2 deformation (2018, result): “te the methods, including diﬀerences from the standard holographic RG, but otherwise stands alone from the rest of the paper and can be skipped. The ﬁnal answer is equivalent to results found in e.g. [4,5,14,39], but our approach is to add nonlinear source dependence to the classical action of the E”
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”
Making predictions in the multiverse (2011, background): “In particular, a simple UV cutoff in the boundary theory probably does not correspond to a sharp IR cutoff on the geometry in the bulk except on scales larger than the curvature radius; see [26] for recent progress in addressing this question.”
Generalized holographic quantum criticality at finite density (2011, background): “There are several works that contain a version or elements of the idea of the EHT, [7], although they vary in the focus or philosophy.”
Holographic and Wilsonian renormalization groups (2010, background): “[37, 38] also takes a Wilsonian approach to transport calculations, and Refs.”
Light-front holographic QCD and emerging confinement (2014, background): “A particularly interesting example, and a line of research worth pursuing, is the holographic flow of boundary theories to AdS2 geometry in the infrared [360, 361, 362], since its dual one-dimensional conformal quantum field theory is realized as conformal quantum mechanics (Sect.”
Strongly correlated quantum fluids: ultracold quantum gases, quantum chromodynamic plasmas and holographic duality (2012, positive): “This holographic renormalization [344, 345, 346, 347, 335, 348] is simply the bulk realization of the UV renormalization of the boundary QFT.”
Bulk and transhorizon measurements in AdS/CFT (2012, positive): “The holographic analog of the Wilsonian renormalization group [49, 50] suggests a framework for this.”
Coadjoint orbit action of Virasoro group and two-dimensional quantum gravity dual to SYK/tensor models (2017, positive): “Together with the natural identification of 1/ζ, for small ζ, with a Wilsonian floating cut-off Λ (to be distinguished from the bare cut-off Λ0 = 1/δ, see [41, 42], also [43]), we find δg/ζ ∼ Λ/J = 1/J̄ , where J̄ = J/Λ is the dimensionless coupling.”
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].”