Quadratic action for type IIB supergravity on $AdS_5\times S^5$

TL;DR

This work provides a complete derivation of the bulk quadratic action for all physical fields of type IIB supergravity on $AdS_5\\times S^5$, starting from the covariant action with auxiliary fields and systematically determining the necessary boundary terms for AdS/CFT. By expanding the fields in spherical harmonics and carefully decoupling sectors, the authors obtain the spectra of bosonic and fermionic modes, with the gravitational sector including a massless graviton and massive traceless tensor modes that reproduce known KRNGM results. They also introduce explicit boundary contributions for the antisymmetric and fermionic fields to yield conformally invariant two-point functions, enabling proper AdS/CFT correlator normalization. The results lay groundwork for extending to higher-order interactions and to other AdS backgrounds, advancing the covariant formulation of IIB supergravity in holographic contexts.

Abstract

The quadratic action for physical fields of type IIB supergravity model on $AdS_5\times S^5$ is derived starting from the recently found covariant action. All boundary terms that have to be added to the action to be used in the AdS/CFT correspondence are determined.