Holographic Renormalization

TL;DR

This paper develops a systematic method for holographic renormalization of RG flows in AdS/CFT, enabling finite correlation functions and satisfying Ward identities, with explicit calculations for specific supergravity models.

Contribution

It introduces a comprehensive holographic renormalization procedure for asymptotically AdS domain walls, including explicit examples from supergravity theories.

Findings

Finite, well-behaved correlators at coincident points.

Explicit 2-point functions for vector currents and scalar operators.

New insights into stress tensor sector correlations.

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.