Understanding the holographic principle via RG flow

Abstract

This is a review of some recent works which demonstrate how the classical equations of gravity in AdS themselves hold the key to understanding their holographic origin in the form of a strongly coupled large $N$ QFT whose algebra of local operators can be generated by a few (single-trace) elements. I discuss how this can be realised by reformulating Einstein's equations in AdS in the form of a non-perturbative RG flow that further leads to a new approach towards constructing strongly interacting QFTs. In particular, the RG flow can self-determine the UV data that are otherwise obtained by solving classical gravity equations and demanding that the solutions do not have naked singularities. For a concrete demonstration, I focus on the hydrodynamic limit in which case this RG flow connects the AdS/CFT correspondence with the membrane paradigm, and also reproduces the known values of the dual QFT transport coefficients.

arXiv comment19 pages; invited review to IJMPA

References in corpus (33)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• The World as a Hologram
• The Dynamics of General Relativity
• A Stress Tensor for Anti-de Sitter Gravity
• The holographic principle
• Shear viscosity of strongly coupled N=4 supersymmetric Yang-Mills plasma
• Supergravity and a Confining Gauge Theory: Duality Cascades and $\chi$SB-Resolution of Naked Singularities
• Nonlinear Fluid Dynamics from Gravity
• Entanglement Renormalization and Holography
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• On the Holographic Renormalization Group
• Gravitation from Entanglement in Holographic CFTs
• Holographic and Wilsonian Renormalization Groups
• Holography and the Weyl anomaly
• Hydrodynamic gradient expansion in gauge theory plasmas
• Entropy of Null Surfaces and Dynamics of Spacetime
• Wilsonian Approach to Fluid/Gravity Duality
• Holography of Gravitational Action Functionals
• Entanglement, Holography and Causal Diamonds
• Coupling hydrodynamics to nonequilibrium degrees of freedom in strongly interacting quark-gluon plasma
• Hydrodynamics, resurgence and trans-asymptotics
• Diffeomorphisms, Anomalies and the Fefferman-Graham Ambiguity
• Generalized Israel Junction Conditions for a Fourth-Order Brane World
• The unconditional RG flow of the relativistic holographic fluid
• A semi-holographic model for heavy-ion collisions
• Spacetime emergence via holographic RG flow from incompressible Navier-Stokes at the horizon
• On the universal hydrodynamics of strongly coupled CFTs with gravity duals
• Holography as a highly efficient RG flow I: Rephrasing gravity
• Holography as a highly efficient RG flow II: An explicit construction
• An AdS/CFT Connection between Boltzmann and Einstein
• Homogeneous Relaxation at Strong Coupling from Gravity

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• Illustrated study of the semi-holographic non-perturbative framework
• DC conductivity with external magnetic field in hyperscaling violating geometry
• Developing local RG: quantum RG and BFSS
• Holographic Gubser flow: A combined analytic and numerical study
• How Gubser flow ends in a holographic conformal theory
• Holographic RG from ERG: Locality and General Coordinate Invariance in the Bulk