Holographic renormalization for coincident Dp-branes

TL;DR

This paper develops a holographic renormalization procedure for the supergravity sector of coincident Dp-branes, deriving counterterms to regularize the bulk action and compute dual field theory one-point functions.

Contribution

It introduces a non-linear asymptotic expansion for graviton and dilaton deformations and derives counterterms for both linear and non-linear sphere deformations in the Dp-brane holographic setup.

Findings

Derived finite renormalized bulk action.

Constructed asymptotic expansions for deformations.

Identified counterterms for sphere deformations.

Abstract

We consider holographic renormalization for the decoupling limit of coincident Dp-branes. We truncate the theory to the supergravity sector which is homogeneous on the (8-p)-sphere and carries only RR electric (p+2)-flux, leaving a graviton and two scalar degrees of freedom associated to the dilaton and the sphere radius. We non-linearly construct the asymptotic graviton and dilaton deformations - the analog of the Graham-Fefferman expansion for AdS/CFT - and compute counterterms to give a finite renormalized bulk action and dual one point functions. Restricting to linear deformations we find additional counterterms to include the remaining sphere deformations which strongly deform the asymptotic behaviour.