For m²L²=-2 in AdS black holes with integrable mixed boundary conditions, the cubic coefficient in the near-boundary expansion of the solution-dependent W(φ) is fixed by the boundary deformation to ensure a well-posed variational principle and finite renormalized action.
Holographic Renormalization and Ward Identities with the Hamilton-Jacobi Method
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abstract
A systematic procedure for performing holographic renormalization, which makes use of the Hamilton-Jacobi method, is proposed and applied to a bulk theory of gravity interacting with a scalar field and a U(1) gauge field in the Stueckelberg formalism. We describe how the power divergences are obtained as solutions of a set of "descent equations" stemming from the radial Hamiltonian constraint of the theory. In addition, we isolate the logarithmic divergences, which are closely related to anomalies. The method allows to determine also the exact one-point functions of the dual field theory. Using the other Hamiltonian constraints of the bulk theory, we derive the Ward identities for diffeomorphisms and gauge invariance. In particular, we demonstrate the breaking of U(1)_R current conservation, recovering the holographic chiral anomaly recently discussed in hep-th/0112119 and hep-th/0202056.
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Holographic renormalization and the variational problem for mixed boundary conditions via a solution-dependent superpotential-like function
For m²L²=-2 in AdS black holes with integrable mixed boundary conditions, the cubic coefficient in the near-boundary expansion of the solution-dependent W(φ) is fixed by the boundary deformation to ensure a well-posed variational principle and finite renormalized action.