Consistency Conditions for Holographic Duality

Abstract

We show that if the beta functions of a field theory are given by the gradient of a certain potential on the space of couplings, a gravitational background in one more dimension can express the renormalization group (RG) flow of the theory. The field theory beta functions and the gradient flow constraint together reconstruct the second order spacetime equations of motion. The RG equation reduces to the conventional gravitational computation of the spacetime quasilocal stress tensor, and a c-theorem holds true as a consequence of the Raychaudhuri equation. Conversely, under certain conditions, if the RG evolution of a field theory possesses a monotonic c-function, the flow of couplings can be expressed in terms of a higher dimensional gravitational background.

LaTeX, 14 pages

References in corpus (11)

• On the Holographic Renormalization Group
• Gravitational Stability and Renormalization-Group Flow
• RG-Flow, Gravity and the Cosmological Constant
• The Holographic Principle for General Backgrounds
• On geodesic propagators and black hole holography
• Surface counterterms and boundary stress-energy tensors for asymptotically non-anti-de Sitter spaces
• Finite Action in d5 Gauged Supergravity and Dilatonic Conformal Anomaly for Dual Quantum Field Theory
• Holography, a covariant c-function, and the geometry of the renormalization group
• Notes on Fluctuations and Correlation Functions in Holographic Renormalization Group Flows
• A Note On Relation Between Holographic RG Equation And Polchinski's RG Equation
• AdS-Flows and Weyl Gravity

Cited by in corpus (21)

• The holographic principle
• Mass, Entropy and Holography in Asymptotically de Sitter Spaces
• The Raychaudhuri equations: a brief review
• Black holes with topologically nontrivial AdS asymptotics
• Deconstructing de Sitter
• Tall tales from de Sitter space I: Renormalization group flows
• Finite Action in d5 Gauged Supergravity and Dilatonic Conformal Anomaly for Dual Quantum Field Theory
• Four Dimensional Conformal Supergravity From AdS Space
• Anatomy of Two Holographic Renormalization Group Flows
• Dynamics of a Stabilized Radion and Duality
• A Field-theoretical Interpretation of the Holographic Renormalization Group
• Holographic renormalization group and conformal anomaly for AdS_9/CFT_8 correspondence
• Asymptotically de Sitter dilatonic space-time, holographic RG flow and conformal anomaly from (dilatonic) dS/CFT correspondence
• Holographic Renormalization Group with Fermions and Form Fields
• Instantons, the Information Metric, and the AdS/CFT Correspondence
• Scheme-dependence of holographic conformal anomaly in d5 gauged supergravity with non-trivial bulk potential
• The Jarzynski Identity and the AdS/CFT Duality
• Deconstruction and Holography
• On the Holographic RG-flow and the Low-energy, Strong Coupling, Large N Limit
• The clash between de Sitter and anti-de Sitter space
• Gradient Flow and Holography from a Local Wilsonian Cutoff