More on counterterms in the gravitational action and anomalies

Abstract

The addition of boundary counterterms to the gravitational action of asymptotically anti-de Sitter spacetimes permits us to define the partition function unambiguously without background subtraction. We show that the inclusion of p-form fields in the gravitational action requires the addition of further counterterms which we explicitly identify. We also relate logarithmic divergences in the action dependent on the matter fields to anomalies in the dual conformal field theories. In particular we find that the anomaly predicted for the correlator of the stress energy tensor and two vector currents in four dimensions agrees with that of the $\mathcal{N}=4$ superconformal SU(N) gauge theory.

arXiv comment18 pages, ReVTeX, references and section added, typos corrected

Cited by in corpus (30)

• Holographic Superconductors with Various Condensates
• Holographic Entanglement Entropy in Lovelock Gravities
• Further Evidence for Lattice-Induced Scaling
• Charged Magnetic Brane Solutions in AdS_5 and the fate of the third law of thermodynamics
• General (Anti-)de Sitter Black Holes in Five Dimensions
• DC Conductivity of Magnetised Holographic Matter
• Generalised global symmetries in holography: magnetohydrodynamic waves in a strongly interacting plasma
• Supersymmetric gauge theories on squashed five-spheres and their gravity duals
• Chiral hydrodynamics in strong external magnetic fields
• Quasinormal modes of charged magnetic black branes & chiral magnetic transport
• The gravity dual of supersymmetric gauge theories on a squashed $S^1\times S^3$
• No hair conjecture, nonabelian hierarchies and anti-de Sitter spacetime
• Conformal field theories in $d=4$ with a helical twist
• Holographic superconductor with momentum relaxation and Weyl correction
• Static axially symmetric solutions of Einstein-Yang-Mills equations with a negative cosmological constant: black hole solutions
• Scanning the Parameter Space of Holographic Superconductors
• AdS_5 solutions in Einstein--Yang-Mills--Chern-Simons theory
• Holographic Renormalization Group with Fermions and Form Fields
• Squashed, magnetized black holes in $D=5$ minimal gauged supergravity
• Topological AdS/CFT
• Holographic hydrodynamics: models and methods
• Anomalous transport from holography: Part II
• Cosmological monopoles and non-abelian black holes
• Global monopoles, cosmological constant and maximal mass conjecture
• Magnetic solutions in AdS${}_5$ and trace anomalies
• AdS${}_5$ magnetized solutions in minimal gauged supergravity
• Holographic Charged Fluid with Chiral Electric Separation Effect
• AdS${}_5$ rotating non-Abelian black holes
• Topological confinement in Skyrme holography
• Holographic Stress Tensor for Kerr-AdS Black Holes and Local Failure on IR-UV Connection