Some Cubic Couplings in Type IIB Supergravity on $AdS_5\times S^5$ and Three-point Functions in SYM_4 at Large N

TL;DR

This work derives all cubic couplings in type IIB supergravity on $AdS_5\times S^5$ that involve two scalar fields $s^I$ (mixtures of the $S^5$ five-form and the trace of the sphere graviton) and computes the corresponding three-point functions in ${\cal N}=4$ SYM at large $N$ in the supergravity limit. It shows that the $s^I$ correspond to extended chiral primary operators (CPOs) containing non-chiral double-trace pieces, and employs field redefinitions to remove higher-derivative terms, yielding explicit vertices with scalars, tensors, and vectors. The paper provides the vertices $S_{tss}$, $S_{ss\phi}$, $S_{ssg}$, and $S_{ssv}$ along with their normalized three-point functions, computed via standard AdS/CFT bulk-to-boundary propagators and the FMMR formalism. Together, these results clarify the operator content mapped by $s^I$ and lay groundwork for higher-point functions and quartic couplings, while highlighting open questions about direct CPO correspondences and extensions to other AdS compactifications.

Abstract

All cubic couplings in type IIB supergravity on $AdS_5\times S^5$ that involve two scalar fields $s^I$ that are mixtures of the five form field strength on $S^5$ and the trace of the graviton on $S^5$ are derived by using the covariant equations of motion and the quadratic action for type IIB supergravity on $AdS_5\times S^5$. All corresponding three-point functions in SYM$_4$ are calculated in the supergravity approximation. It is pointed out that the scalars $s^I$ correspond not to the chiral primary operators in the ${\cal N}=4$ SYM but rather to a proper extension of the operators.