Integrating out geometry: Holographic Wilsonian RG and the membrane paradigm

Abstract

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.

21 pages, 2 figures; references added, minor changes

References in corpus (14)

• Nonlinear Fluid Dynamics from Gravity
• Viscosity, Black Holes, and Quantum Field Theory
• Holographic and Wilsonian Renormalization Groups
• Gravity & Hydrodynamics: Lectures on the fluid-gravity correspondence
• Boundary Conditions and Dualities: Vector Fields in AdS/CFT
• Wilsonian Approach to Fluid/Gravity Duality
• Holographic renormalization as a canonical transformation
• Shear Modes, Criticality and Extremal Black Holes
• Deconstructing holographic liquids
• Large N Field Theory and AdS Tachyons
• Holography and the sound of criticality
• Holographic description of quantum field theory
• Multitrace deformations, Gamow states, and Stability of AdS/CFT
• Holographic description of large N gauge theory

Cited by in corpus (81)

• Chaos in AdS${}_2$ holography
• $T\bar{T}$ and the mirage of a bulk cutoff
• Quantum Information in Holographic Duality
• Light-sheets and AdS/CFT
• Null Geodesics, Local CFT Operators and AdS/CFT for Subregions
• Exotic RG Flows from Holography
• CFT dual of the AdS Dirichlet problem: Fluid/Gravity on cut-off surfaces
• Holographic non-Fermi liquid fixed points
• Open quantum systems and Schwinger-Keldysh holograms
• Generalised global symmetries in holography: magnetohydrodynamic waves in a strongly interacting plasma
• Membrane theory of entanglement dynamics from holography
• de Sitter extremal surfaces
• Linearized fluid/gravity correspondence: from shear viscosity to all order hydrodynamics
• Coarse Grained Quantum Dynamics
• Charge transport by holographic Fermi surfaces
• On the stability of gravity with Dirichlet walls
• The Holographic Geometry of the Renormalization Group and Higher Spin Symmetries
• Gravitational path integral from the $T^2$ deformation
• Emergent IR dual 2d CFTs in charged AdS5 black holes
• Holographic entanglement entropy and the internal space
• Aspects of Current Correlators in Holographic Theories with Hyperscaling Violation
• The Exact Renormalization Group and Higher-spin Holography
• Quantum criticality and duality in the SYK/AdS${}_2$ chain
• Towards a general fluid/gravity correspondence
• Holographic Forced Fluid Dynamics in Non-relativistic Limit
• Cutoff Dependence and Complexity of the CFT${}_2$ Ground State
• Deep learning black hole metrics from shear viscosity
• Disordered Holographic Systems I: Functional Renormalization
• Cutoff $\mathrm{Ad}{\mathrm{S}}_3$ versus $\mathrm{T}\bar{\mathrm{T}}$ $\mathrm{CF}{\mathrm{T}}_2$ in the large central charge sector: correlators of energy-momentum tensor
• Fluid/gravity duality with Petrov-like boundary condition in a spacetime with a cosmological constant
• Hyperscaling violating black hole solutions and Magneto-thermoelectric DC conductivities in holography
• S-parameter, Technimesons, and Phase Transitions in Holographic Tachyon DBI Models
• Holographic Interpretation of Acoustic Black Holes
• An emergent geometric description for a topological phase transition in the Kitaev superconductor model
• Semi-Holographic Quantum Criticality
• Counterterms, critical gravity and holography
• On c-theorems in arbitrary dimensions
• Membrane paradigm for Einstein-Gauss-Bonnet gravity
• (A)dS Holography with a Cut-off
• A non-perturbative field theory approach for the Kondo effect: Emergence of an extra dimension and its implication for the holographic duality conjecture
• The Petrov-like boundary condition at finite cutoff surface in Gravity/Fluid duality
• Illustrated study of the semi-holographic non-perturbative framework
• Holography as a highly efficient RG flow I: Rephrasing gravity
• Holographic RG flow of thermo-electric transports with momentum dissipation
• Into the Bulk: A Covariant Approach
• Holographic Wilson's RG
• Holography as a highly efficient RG flow II: An explicit construction
• Fluid/gravity correspondence for massive gravity
• Zero sound and higher-form symmetries in compressible holographic phases
• Time-dependent $NAd{S}_2$ holography with applications
• Consistency relations and conservation of $\zeta$ in holographic inflation
• Entanglement of scales as a possible mechanism for decoherence and thermalization in relativistic heavy ion collisions
• Geometric encoding of renormalization group $\beta -$functions in an emergent holographic dual description
• Bulk Locality and Asymptotic Causal Diamonds
• Constraining Non-Relativistic RG Flows with Holography
• Emergent dual holographic description as a non-perturbative generalization of the Wilsonian renormalization group
• Increase of the Energy Necessary to Probe Ultraviolet Theories Due to the Presence of a Strong Magnetic Field
• Wilsonian RG-flow approach to holographic transport with momentum dissipation
• Stochastic quantization and holographic Wilsonian renormalization group of scalar theories with arbitrary mass
• Stochastic quantization and holographic Wilsonian renormalization group of free massive fermion
• 4-point function from conformally coupled scalar in AdS${}_6$
• Echoes in the Kerr/CFT correspondence
• Higher-spin realization of a dS static patch/cut-off CFT correspondence
• Pair production from Reissner-Nordström-anti-de Sitter black holes
• Testing the membrane paradigm with holography
• Dimensional regularization for holographic RG flows
• Transport Coefficients for Holographic Hydrodynamics at Finite Energy Scale
• Sine-Gordon Theory : Entanglement entropy and holography
• Constraints on beta functions in field theories
• Beta-Functions and RG flows for Holographic QCD with Heavy and Light Quarks: Isotropic case
• Holographic Wilsonian Renormalization and Chiral Phase Transitions
• Cutoff Function in Holographic RG Flow
• Higher order curvature corrections and holographic renormalization group flow
• Holographic RG from ERG: Locality and General Coordinate Invariance in the Bulk
• Entanglement Renormalization of a $T\bar{T}$-deformed CFT
• On holographic Wilsonian renormalization group of massive scalar theory with its self-interactions in AdS
• Stochastic quantization and holographic Wilsonian renormalization group of conformally coupled scalar in AdS${}_4$
• Retarded Green's Function from Rotating AdS Black Holes: Emergent CFT${}_2$ and Viscosity
• First order formalism of holographic Wilsonian renormalization group: Langevin equation
• Metallic and antiferromagnetic fixed points from gravity
• Time evolving fluid from Vaidya spacetime