On the Holographic Renormalization Group

Abstract

We propose a direct correspondence between the classical evolution equations of 5-d supergravity and the renormalization group (RG) equations of the dual 4-d large $N$ gauge theory. Using standard Hamilton-Jacobi theory, we derive first order flow equations for the classical supergravity action $S$, that take the usual form of the Callan-Symanzik equations, including the corrections due to the conformal anomaly. This result gives direct support for the identification of $S$ with the quantum effective action of the gauge theory. In addition we find interesting new relations between the beta-functions and the counterterms that affect the 4-d cosmological and Newton constant.

14 pages, no figures

References in corpus (33)

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• Large N Field Theories, String Theory and Gravity
• The Cosmological Constant
• The Holographic Weyl anomaly
• Modulus Stabilization with Bulk Fields
• Supergravity description of field theories on curved manifolds and a no go theorem
• Modeling the fifth dimension with scalars and gravity
• Towards the large N limit of pure N=1 super Yang Mills
• The Holographic Bound in Anti-de Sitter Space
• Novel Local CFT and Exact Results on Perturbations of N=4 Super Yang Mills from AdS Dynamics
• Bulk vs. Boundary Dynamics in Anti-de Sitter Spacetime
• Gravitational Stability and Renormalization-Group Flow
• Holography and Compactification
• Self-tuning flat domain walls in 5d gravity and string theory
• Spacetime and the Holographic Renormalization Group
• The wall of the cave
• A remark on the AdS/CFT correspondence and the renormalization group flow
• RG-Flow, Gravity and the Cosmological Constant
• Geometric Holography, the Renormalization Group and the c-Theorem
• RG Fixed Points in Supergravity Duals of 4-d Field Theory and Asymptotically AdS Spaces
• Anatomy of Two Holographic Renormalization Group Flows
• Curvature Singularities: the Good, the Bad, and the Naked
• Notes on Fluctuations and Correlation Functions in Holographic Renormalization Group Flows
• Cubic couplings in D=6 N=4b supergravity on AdS_3\times S^3
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• A Note On Relation Between Holographic RG Equation And Polchinski's RG Equation
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• On Open/Closed String Duality
• Field theory insight from the AdS/CFT correspondence
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Cited by in corpus (475)

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• On $Ad{S}_2$ holography from redux, renormalization group flows and $c$-functions
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• From sources to initial data and back again: on bulk singularities in Euclidean AdS/CFT
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• Outer Entropy and Quasilocal Energy
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• Holographic RG flows on Squashed $S^3$
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• Universal stress-tensor correlation functions of strongly coupled conformal fluids
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• Graviton multi-point functions at the AdS boundary
• Higher order curvature corrections and holographic renormalization group flow
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• Wilson loops in exact holographic RG flows at zero and finite temperature
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• Quantum Holographic Entanglement Entropy to All Orders in $1/N$ Expansion
• Hamilton-Jacobi formulation of holographic Entanglement Entropy
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• From Feynman graphs to Witten diagrams
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• Renormalization group flow to effective quantum mechanics at IR in an emergent dual holographic description for spontaneous chiral symmetry breaking
• Geometric realization of stress-tensor deformed field theory
• QCD, with Strings Attached
• Information geometry encoded in bulk geometry
• Thermodynamics of spinning AdS4 black holes in gauged supergravity
• The Riches of the Elementary Fluxbrane Solution
• On Functional Hamilton-Jacobi and Schrödinger Equations and Functional Renormalization Group
• Holographic renormalization group flows in two-dimensional gravity and $AdS$ black holes
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• Holography, Fractals and the Weyl Anomaly
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• Monotonicity of RG flow in emergent dual holography of worldsheet nonlinear $\sigma$ model
• Holographic renormalization by Hamilton-Jacobi formulation with generated ansatz
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• On Effective Actions from Holography
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• Statistical entropy of three-dimensional q-deformed Kerr-de Sitter space
• A Note on Efimov Nonlocal and Nonpolynomial Quantum Scalar Field Theory
• $N$-point functions of strongly coupled fluids dual to generalized higher-derivative theories of gravity
• Sonic velocity in holographic fluids and its applications
• Closed String Brane-Like States, Brane Bound States and Noncommutative Branes
• Comments on contact terms and conformal manifolds in the AdS/CFT correspondence
• Retarded Green's Function from Rotating AdS Black Holes: Emergent CFT${}_2$ and Viscosity
• Exact Mappings in Condensed Matter Physics
• Metallic and antiferromagnetic fixed points from gravity
• Periapsis shift and deflection of light by hairy black holes
• Gradient flows for $\beta$ functions via multi-scale renormalization group equations
• Evolution of Lifshitz metric anisotropies in Einstein-Proca theory under the Ricci-DeTurck flow
• Gradient Flow and Holography from a Local Wilsonian Cutoff
• Holographic entanglement renormalisation for fermionic quantum matter
• Cosmological constant as quantum error correction from generalised gauge invariance in double field theory
• Holography and (1+1)-dimension non-relativistic Quantum Mechanics
• Holographic RG and Exact RG in O(N) Model
• A theory of time based on wavefunction collapse
• Holographic trace anomaly at finite temperature
• First order formalism of holographic Wilsonian renormalization group: Langevin equation
• Casimir Energy of the Universe and New Regularization of Higher Dimensional Quantum Field Theories
• $SO(1,d+1)$ symmetry of the Exact RG equation
• Probing sine dilaton gravity with flow central charge
• Constructing CFTs from AdS flows
• Renormalization group flow, Entropy and Eigenvalues
• Anomaly matching condition in two-dimensional systems
• Ising Model on Twisted Lattice and Holographic RG flow