An explicit covariant formula for thermodynamic volume is derived that universally decomposes into explicit Lagrangian coupling dependence plus dynamical field response contributions.
Holographic Renormalization
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We systematically develop the procedure of holographic renormalization for RG flows dual to asymptotically AdS domain walls. All divergences of the on-shell bulk action can be cancelled by adding covariant local boundary counterterms determined by the near-boundary behavior of bulk fields. This procedure defines a renormalized action from which correlation functions are obtained by functional differentiation. The correlators are finite and well behaved at coincident points. Ward identities, corrected for anomalies, are satisfied. The correlators depend on parts of the solution of the bulk field equations which are not determined by near-boundary analysis. In principle a full nonlinear solution is required, but one can solve linearized fluctuation equations to define a bulk-to-boundary propagator from which 2-point correlation functions are easily obtained. We carry out the procedure explicitly for two known RG flows obtained from the maximal gauged D=5 supergravity theory, obtaining new results on correlators of vector currents and related scalar operators and giving further details on a recent analysis of the stress tensor sector.
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Bulk-to-boundary correlators for spin-s operators in Poincaré-invariant massless theories are linear superpositions of ISO(2)-fixed tensor structures mapped to non-crossing double-line diagrams that are tensor products of loop diagrams, extrapolating to type Ib multiplets in CCFT generated by Wigner
Holographic RG flow on a 2D CFT induces JT gravity with bulk lapse as dilaton and recovers TTbar deformation in the Fefferman-Graham limit.
Holographic analysis of Romans supergravity solutions with Abelian magnetic flux yields a family of confining 4D duals featuring a flux-driven first-order deconfinement transition and two parametrically light, nearly degenerate scalar bound states near the transition.
Derives holographic one-point functions, stress tensor and Ward identities for defects in AdS5 and AdS6 from AdS2×S2, AdS2×S3 and AdS3×S2 backgrounds in Romans supergravity.
Background subtraction for black hole thermodynamics is valid and equivalent to Iyer-Wald in matter-coupled gravity theories, with smooth performance in examples but subtleties for certain matter fields.
The paper organizes important open questions in quantum gravity and quantum information into four themes without presenting new results or derivations.
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