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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abstract
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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Holographic duals from Romans supergravity with Abelian magnetic flux yield confining 4D theories with a flux-driven zero-temperature deconfinement transition and a spectrum dominated by two nearly degenerate light scalars, one a dilaton.
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.
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Explicit and covariant formula for thermodynamic volume in extended black hole thermodynamics
An explicit covariant formula for thermodynamic volume is derived that universally decomposes into explicit Lagrangian coupling dependence plus dynamical field response contributions.
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Bound states and deconfinement from Romans supergravity with magnetic flux
Holographic duals from Romans supergravity with Abelian magnetic flux yield confining 4D theories with a flux-driven zero-temperature deconfinement transition and a spectrum dominated by two nearly degenerate light scalars, one a dilaton.
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Validity of the Background Subtraction Method for Black Hole Thermodynamics in Matter-Coupled Gravity Theories
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.