Holographic conformal anomaly with bulk scalars potential from d3 and d5 gauged supergravity

TL;DR

This paper calculates holographic conformal anomalies in d3 and d5 gauged supergravity with arbitrary scalar potentials, linking bulk scalar dynamics to boundary conformal anomalies in the AdS/CFT framework.

Contribution

It derives explicit formulas for d2 and d4 holographic conformal anomalies considering general scalar potentials in maximally SUSY gauged supergravity models.

Findings

Derived d2 and d4 conformal anomalies depending on scalar potential.

Reproduced known anomaly for maximally SUSY super Yang-Mills in specific limit.

Demonstrated the connection between bulk scalar dynamics and boundary conformal anomalies.

Abstract

d3 and d5 maximally SUSY gauged supergravity is considered in the parametrization (flow) of full scalar coset where the kinetic term for scalars takes the standard field theory form and the bulk potential is an arbitrary one subject to consistent parametrization. From such SG duals we calculate d2 and d4 holographic conformal anomaly which depends on bulk scalars potential. AdS/CFT correspondence suggests that such SG side conformal anomaly should be identified with (non-perturbative) QFT conformal anomaly (taking account of radiative corrections) for the theory living on the boundary of AdS space. In the limit of constant bulk potential and single scalar, d4 result reproduces the known exact conformal anomaly corresponding to maximally SUSY super Yang-Mills theory coupled to ${\cal N}=4$ conformal supergravity.