Extrinsic holographic renormalization for a scalar field
Year: 2024
Type: article
Abstract: In the context of the holographic correspondence, we introduce a purely extrinsic renormalization prescription, exemplified with the case of a minimally-coupled scalar field in AdS space. The counterterms depend only on the field and its radial derivatives. This would seem to conflict with the Dirichlet variational principle, but we show that consistency follows from the fact that the asymptotic structure of asymptotically locally AdS spacetimes requires not only the leading, but also all of the subleading non-normalizable modes to be fixed as a boundary condition. Crucially, as seen from a path integral definition of the bulk partition function involved in the standard GKPW formula, this condition is valid away from the saddle. We find that the extrinsic renormalization prescription is maximally efficient when the scalar field is massless, which is suggestive of a connection with the Kounterterm method for renormalization of pure gravity.
Source: Nuclear Physics B
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Awards: CONFORMAL RENORMALIZATION AND ITS APPLICATIONS IN HOLOGRAPHY, TOPOLOGICALLY NONTRIVIAL CONFIGURATIONS AND NONPERTURBATIVE EFFECTS, G5737508896, G6958583472, G7302129035, CONSERVATION LAWS IN GRAVITY UNDER FRAME TRANSFORMATIONS DUAL DIFFEOMORPHISMS AND NEW APPLICATIONS, ENTANGLEMENT ENTROPY AND HOLOGRAPHY IN HIGHER CURVATURE ADS GRAVITY
OpenAlex ID: W4404770489