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 paper derives cubic couplings in type IIB supergravity on $AdS_5\times S^5$ involving scalar fields and computes the corresponding three-point functions in ${\cal N}=4$ SYM, revealing an extended operator correspondence.

Contribution

It provides explicit derivations of cubic couplings involving mixed scalar fields and computes related three-point functions, extending the understanding of operator mappings in AdS/CFT.

Findings

Derived all relevant cubic couplings involving scalar fields.

Calculated three-point functions in SYM$_4$ from supergravity.

Identified that scalars correspond to extended operators, not just chiral primaries.

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.