Trace Anomaly and Counterterms in Designer Gravity

Abstract

We construct concrete counterterms of the Balasubramanian-Kraus type for Einstein-scalar theories with designer gravity boundary conditions in AdS${}_4$, so that the total action is finite on-shell and satisfy a well defined variational principle for an arbitrary scalar field potential. We focus on scalar fields with the conformal mass, $m^2=-2l^{-2}$, and show that the holographic mass matches the Hamiltonian mass for any boundary conditions. We compute the trace anomaly of the dual field theory in the generic case, as well as when there exist logarithmic branches of non-linear origin. As expected, the anomaly vanishes for the boundary conditions that are AdS invariant. When the anomaly does not vanish, the dual stress tensor describes a thermal gas with an equation of state related to the boundary conditions of the scalar field. When the anomaly vanishes, we recover the dual theory of a massless thermal gas. As an application of the formalism, we consider a general family of exact hairy black hole solutions that, for some particular values of the parameters in the moduli potential, contains solutions of four-dimensional gauged $\mathcal{N}=8$ supergravity and its $\omega$-deformation. Using the AdS/CFT duality dictionary, they correspond to triple trace deformations of the dual field theory.

26 pages, no figures v2: title changed, refs. added, matches the published version

References in corpus (82)

• Gauge Theory Correlators from Non-Critical String Theory
• A Stress Tensor for Anti-de Sitter Gravity
• 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
• Lecture Notes on Holographic Renormalization
• Holographic Renormalization
• Surface Terms as Counterterms in the AdS/CFT Correspondence
• Black Hole Entropy Function and the Attractor Mechanism in Higher Derivative Gravity
• Bulk vs. Boundary Dynamics in Anti-de Sitter Spacetime
• On weakly turbulent instability of anti-de Sitter space
• Black Hole Entropy Function, Attractors and Precision Counting of Microstates
• Holographic Probes of Anti-de Sitter Spacetimes
• Asymptotically Anti-de Sitter Space-times: Conserved Quantities
• Mass, Entropy and Holography in Asymptotically de Sitter Spaces
• Multi-Trace Operators, Boundary Conditions, And AdS/CFT Correspondence
• String Theory and Classical Absorption by Threebranes
• Rotating Attractors
• Asymptotically Anti-de Sitter spacetimes and their stress energy tensor
• Exact black hole solution with a minimally coupled scalar field
• Dynamics in Non-Globally-Hyperbolic Static Spacetimes III: Anti-de Sitter Spacetime
• Stress Tensors and Casimir Energies in the AdS/CFT Correspondence
• Black holes and asymptotics of 2+1 gravity coupled to a scalar field
• Multi-Trace Deformations in AdS/CFT: Exploring the Vacuum Structure of the Deformed CFT
• Comparison between various notions of conserved charges in asymptotically AdS-spacetimes
• Absorption by Branes and Schwinger Terms in the World Volume Theory
• Entropy Function for Heterotic Black Holes
• Holographic Renormalization of Asymptotically Flat Spacetimes
• Black Holes with Scalar Hair and Asymptotics in N=8 Supergravity
• Evidence for a family of SO(8) gauged supergravity theories
• Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields
• Towards a Big Crunch Dual
• Boson Stars in AdS
• Asymptotically Anti-de Sitter spacetimes and scalar fields with a logarithmic branch
• Designer Gravity and Field Theory Effective Potentials
• AdS Dyonic Black Hole and its Thermodynamics
• Conformal Anomaly for Dilaton Coupled Theories from AdS/CFT Correspondence
• Action, Mass and Entropy of Schwarzschild-de Sitter black holes and the de Sitter/CFT Correspondence
• Quasilocal Formalism and Black Ring Thermodynamics
• Exact Black Holes and Universality in the Backreaction of non-linear Sigma Models with a potential in (A)dS4
• Dyonic AdS black holes in maximal gauged supergravity
• Boson stars with negative cosmological constant
• Entropy function and attractors for AdS black holes
• Exact asymptotically flat charged hairy black holes with a dilaton potential
• Four-Dimensional Asymptotically AdS Black Holes with Scalar Hair
• (Un)attractor black holes in higher derivative AdS gravity
• Covariant Counterterms and Conserved Charges in Asymptotically Flat Spacetimes
• The N>2 supersymmetric AdS vacua in maximal supergravity
• Energy Bounds in Designer Gravity
• Scalar Hairy Black Holes in General Dimensions
• A New Class of Exact Hairy Black Hole Solutions
• Reissner-Nordstrom-de Sitter black hole, planar coordinates and dS/CFT
• A finite action for three dimensional gravity with a minimally coupled scalar field
• Finite Action in d5 Gauged Supergravity and Dilatonic Conformal Anomaly for Dual Quantum Field Theory
• On attractor mechanism of $Ad{S}_4$ black holes
• On Black Hole Scalar Hair in Asymptotically Anti de Sitter Spacetimes
• Note on counterterms in asymptotically flat spacetimes
• Asymptotic Flatness, Little String Theory, and Holography
• Hairy planar black holes in higher dimensions
• Mass of asymptotically anti-de Sitter hairy spacetimes
• Black holes in $\omega$-defomed gauged $N=8$ supergravity
• Scale Invariant Hairy Black Holes
• Electric/magnetic duality and RG flows in AdS4/CFT3
• Rotating Boson Stars in 2+1 Dimensions
• On new maximal supergravity and its BPS domain-walls
• Moduli flow and non-supersymmetric AdS attractors
• Exact hairy black brane solutions in $Ad{S}_5$ and holographic RG flows
• Slicing and Brane Dependence of the (A)dS/CFT Correspondence
• Quasilocal formalism and thermodynamics of asymptotically flat black objects
• Bootstrapping gravity solutions
• Thermodynamic instability of doubly spinning black objects
• The Holographic Dictionary for Beta Functions of Multi-trace Coupling Constants
• Quasilocal equilibrium condition for black ring
• Black Holes with Primary Hair in gauged N=8 Supergravity
• Moduli and electromagnetic black brane holography
• Asymptotically flat black holes with scalar hair: a review
• Exact formation of hairy planar black holes
• Near horizon data and physical charges of extremal AdS black holes
• Lobotomy of Flux Compactifications
• On the thermodynamics of hairy black holes
• Hairy Black Hole Stability in AdS, Quantum Mechanics on the Half-Line and Holography
• AdS boson stars in string theory

Cited by in corpus (41)

• Probing QCD critical point and induced gravitational wave by black hole physics
• Phases of planar AdS black holes with axionic charge
• Scalar charges and the first law of black hole thermodynamics
• Mass of Kerr-Newman Black Holes in an external magnetic field
• Supersymmetric solitons in gauged $\mathcal{N}=8$ supergravity
• Thermodynamically stable asymptotically flat hairy black holes with a dilaton potential
• Hairy Black Holes and Duality in an Extended Supergravity Model
• Exploring Accelerating Hairy Black Holes in $2+1$ Dimensions: The Asymptotically Locally Anti-de Sitter Class and its Holography
• Universal Formula for the Holographic Speed of Sound
• On Thermodynamics of AdS Black Holes with Scalar Hair
• Black hole evaporation in Conformal (Weyl) gravity
• Hairy Black Hole Chemistry
• Dynamically and thermodynamically stable black holes in Einstein-Maxwell-dilaton gravity
• On the supersymmetry invariance of flat supergravity with boundary
• Black Hole Thermodynamics with Dynamical Lambda
• Holographic Butterfly Effect and Diffusion in Quantum Critical Region
• Hairy AdS Solitons
• The QCD Trace Anomaly at Strong Coupling from M-Theory
• New non-extremal and BPS hairy black holes in gauged $\mathcal{N}=2$ and $\mathcal{N}=8$ supergravity
• New five-dimensional Bianchi type magnetically charged hairy topological black hole solutions in string theory
• Supersymmetric smooth distributions of M2-branes as AdS solitons
• Reentrant phase transitions in Einstein-Maxwell-scalar black holes
• Holographic Renormalization of Einstein-Maxwell-Dilaton Theories
• Holographic renormalization of Horndeski gravity
• Thermodynamically stable asymptotically flat hairy black holes with a dilaton potential: the general case
• Phase transitions of neutral planar hairy AdS black holes
• Exact holographic RG flows in extended SUGRA
• Holographic Renyi entropies from hyperbolic black holes with scalar hair
• On the thermodynamic phase structure of conformal gravity
• Holographic equation of state in fluid/gravity duality
• Revisit to Thermodynamic Relations in the AdS/CMT Models
• Holography of electrically and magnetically charged black branes
• Einstein-Katz action, variational principle, Noether charges and the thermodynamics of AdS-black holes
• Spatially homogeneous black hole solutions in $z=4$ Hořava-Lifshitz gravity in $(4+1)$ dimensions with Nil geometry and $H^2\times R$ horizons
• Thermodynamics of Asymptotically Flat Dyonic Black Holes
• Holography of AdS Hairy Black Holes and Cardy-Verlinde Formula
• Instability of supersymmetric black holes via quantum phase transitions
• Termodinámica de agujeros negros y campos escalares
• Einstein-scalar field solutions in AdS spacetime: clouds, boundary conditions, and scalar multipoles
• Agujeros Negros con Pelo y Dualidad AdS/CFT
• A new energy bound for Einstein-Scalar theory in AlAdS${}_4$ and holographic bound for deformed CFT${}_3$