A Holographic Study of the $a$-theorem and RG Flow in General Quadratic Curvature Gravity

Abstract

We use the holographic language to show the existence of the $a$-theorem for even dimensional CFTs, dual to the AdS space in general quadratic curvature gravity. We find the Wess-Zumino action which is originated from the spontaneous breaking of the conformal symmetry in $d\le 8$, by using a radial cut-off near the AdS boundary. We also study the RG flow and (average) null energy condition in the space of the couplings of theory. In a simple toy model, we find the regions where this holographic RG flow has a monotonic decreasing behavior.

arXiv comment23 pages, 12 figures

References in corpus (41)

• The Holographic Weyl anomaly
• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• On Renormalization Group Flows in Four Dimensions
• Holographic Renormalization
• On the Holographic Renormalization Group
• Holographic c-theorems in arbitrary dimensions
• Gravitational Stability and Renormalization-Group Flow
• Seeing a c-theorem with holography
• How to go with an RG Flow
• The Gravitational Action in Asymptotically AdS and Flat Spacetimes
• The domain-wall/QFT correspondence
• Supersymmetric Gauge Theories and the AdS/CFT Correspondence
• Spacetime and the Holographic Renormalization Group
• The Constraints of Conformal Symmetry on RG Flows
• Fake Supergravity and Domain Wall Stability
• Holography and the Weyl anomaly
• Averaged Null Energy Condition from Causality
• The Supergravity Dual of N=1 Super Yang-Mills Theory
• A remark on the AdS/CFT correspondence and the renormalization group flow
• Correlation Functions in Holographic RG Flows
• Critical Points of D-Dimensional Extended Gravities
• Holographic studies of Einsteinian cubic gravity
• A holographic proof of the averaged null energy condition
• An Exact Holographic RG Flow Between 2d Conformal Fixed Points
• RG flows in d dimensions, the dilaton effective action, and the a-theorem
• Higher Derivative Corrections to R-charged Black Holes: Boundary Counterterms and the Mass-Charge Relation
• Hamilton-Jacobi Counterterms for Einstein-Gauss-Bonnet Gravity
• Holographic RG flows on curved manifolds and quantum phase transitions
• CFT/CFT interpolating RG flows and the holographic c-function
• Causality and a-theorem Constraints on Ricci Polynomial and Riemann Cubic Gravities
• Holographic c-theorems and higher derivative gravity
• On c-theorems in arbitrary dimensions
• Entropy functionals and c-theorems from the second law
• The a-theorem and conformal symmetry breaking in holographic RG flows
• Simple counterterms for asymptotically AdS spacetimes in Lovelock gravity
• Holographic c-theorem and Born-Infeld Gravity Theories
• Holographic Studies of The Generic Massless Cubic Gravities
• Ricci cubic gravity in d dimensions, gravitons and SAdS/Lifshitz black holes
• RG Flows Towards IR Isolated Fixed Points: Some Type 0 Samples
• RG Flow and Thermodynamics of Causal Horizons in Higher-Derivative AdS Gravity

Cited by in corpus (8)

• Renormalized holographic entanglement entropy for Quadratic Curvature Gravity
• Holographic complexity in general quadratic curvature theory of gravity
• Inhomogeneous metrics on complex bundles in Lovelock gravity
• $c$-functions in Higher-derivative Flows Across Dimensions
• Energy of anti-de Sitter black holes in odd-dimensional Quadratic Curvature Gravity
• Higher order curvature corrections and holographic renormalization group flow
• Explicit Entropic Proofs of Irreversibility Theorems for Holographic RG Flows
• Probing sine dilaton gravity with flow central charge