Surface Terms as Counterterms in the AdS/CFT Correspondence

Abstract

We examine the recently proposed technique of adding boundary counterterms to the gravitational action for spacetimes which are locally asymptotic to anti-de Sitter. In particular, we explicitly identify higher order counterterms, which allow us to consider spacetimes of dimensions d<=7. As the counterterms eliminate the need of ``background subtraction'' in calculating the action, we apply this technique to study examples where the appropriate background was ambiguous or unknown: topological black holes, Taub-NUT-AdS and Taub-Bolt-AdS. We also identify certain cases where the covariant counterterms fail to render the action finite, and we comment on the dual field theory interpretation of this result. In some examples, the case of vanishing cosmological constant may be recovered in a limit, which allows us to check results and resolve ambiguities in certain asymptotically flat spacetime computations in the literature.

Revtex, 18 pages. References updated and few typo's fixed. Final version

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• Entropy of Thermal CFTs on Curved Backgrounds
• Asymptotically AdS Magnetic Branes in (n+1)-dimensional Dilaton Gravity
• Dyonic Taub-NUT-AdS: Unconstraint Thermodynamics and Phase Structure
• Euclidean Thermodynamics and Lyapunov Exponents of Einstein-Power-Yang-Mills AdS Black Holes
• Holography for field theory solitons
• On the well-posed variational principle in degenerate point particle systems using embeddings of the symplectic manifold
• Holography of negative energy states
• Asymptotic symmetries of three dimensional gravity and the membrane paradigm
• Confinement and Graded Partition Functions for $\mathcal{N}=4$ SYM
• Higher-Derivative Corrections to Entropy and the Weak Gravity Conjecture in Anti-de Sitter Space
• Entropy of BTZ black strings in the brick wall approach
• A Variational Principle for Radial Flows in Holographic theories
• A holographic stress-energy tensor near the Cauchy horizon inside a rotating black hole
• Subleading corrections to the $S^3$ free energy of necklace quiver theories dual to massive IIA
• Higher-Derivative Supergravity, AdS${}_4$ Holography, and Black Holes
• Higher-Curvature Gravity, Black Holes and Holography
• Holographic 3d $\mathcal{N}=1$ Conformal Manifolds
• Phase Transitions Between Solitons and Black Holes in Asymptotically AdS/$Z_k$ Spaces
• An infinity of black holes
• On black hole thermodynamics with a momentum relaxation
• 7D Randall-Sundrum cosmology, brane-bulk energy exchange and holography
• Deformations of the AdS-Schwarzschild black brane and the shear viscosity of the quark-gluon plasma
• Constant curvature black holes in Einstein AdS gravity: conserved quantities
• Brane Splitting via Quantum Tunneling
• On Penrose inequality in holography
• Complexity as a holographic probe of strong cosmic censorship
• Holographic RG flow triggered by a classically marginal operator
• Graviton multi-point functions at the AdS boundary
• Holographic Duality for three-dimensional Super-conformal Field Theories
• Complexity growth rate, grand potential and partition function
• Quantum Holographic Entanglement Entropy to All Orders in $1/N$ Expansion
• Brown-Teitelboim Instantons and the First Law of Thermodynamics of (Anti) de Sitter Space
• Clumping and quantum order: Quantum gravitational dynamics of NUT charge
• Towards a Holographic Dual of SQCD: Holographic Anomalies and Higher Derivative Gravity
• Counterterms for Static Lovelock Solutions
• Killing spinors on supersymmetric P-branes
• Holographic duality and applications
• Reparameterization Dependence and Holographic Complexity of Black Holes
• Constant curvature black holes in Einstein AdS gravity: Euclidean action and thermodynamics
• Counterterm method and thermodynamics of Hairy Black Holes in a Vector-Tensor theory with Abelian gauge symmetry breaking
• Criticality of Lower Dimensional AdS${}_d$ Black Holes
• Thermodynamics of the 3-dimensional Einstein-Maxwell system
• Entropy Product Formula for Gravitational Instanton
• Vacuum energy in Kerr-AdS black holes
• Virial mass in warped DGP-inspired L(R) gravity
• Thermodynamics and Phase Transitions of NUTty Dyons
• Boundary Conditions in Topological AdS${}_4$/CFT${}_3$
• Partition functions on squashed seven-spheres and holography
• 3-dimensional holographic trace anomaly from AdS/CFT correspondence
• Gravitational Waves in Braneworld Scenarios with AdS Background
• Dyonic Taub-NUT-AdS Spaces: Phase Structures of all Horizon Geometries
• Shape Deformations of Charged Rényi Entropies from Holography
• Wrapped $M5$-branes and complex saddle points
• Bekenstein-Hawking Entropy Products for NUT class of Black Holes in AdS Space
• Kac-Moody Algebras on Soft Group Manifolds
• Dyonic Taub-NUT-AdS Black Branes: Thermodynamics and Phase Diagrams
• Phase transitions in a three-dimensional analogue of Klebanov-Strassler
• Randall-Sundrum Model with a Dilaton Field at Finite Temperature
• Diffusion and instabilities in large-N holographic Fermi liquids: the vector fluctuations of the electron star
• Holography, Supergravity, and the Weak Gravity Conjecture
• Sonic velocity in holographic fluids and its applications
• Meronic Einstein-Yang-Mills black hole in 5D and gravitational spin from isospin effect
• Dirac-Born-Infeld Counter-Term and Black Hole Thermodynamics
• Boundary mutual information in double holography
• Holographic Weyl Anomaly and Kounterterms in AdS gravity
• Agujeros Negros con Pelo y Dualidad AdS/CFT
• Exact Solutions and Black Hole Stability in Higher Dimensional Supergravity Theories