Scalar Quartic Couplings in Type IIB Supergravity on $AdS_5\times S^5$

TL;DR

This paper derives all scalar quartic couplings in type IIB supergravity on AdS_5×S^5, demonstrating their structure, vanishing in extremal cases, and confirming consistency with N=8 supergravity truncation and non-renormalization properties.

Contribution

It provides explicit calculations of scalar quartic couplings in type IIB supergravity, including derivative terms, and proves their consistency with supergravity truncation and non-renormalization conjectures.

Findings

Quartic couplings contain two and four derivatives.

Quartic action vanishes in extremal cases.

Truncation to massless multiplet is consistent.

Abstract

All quartic couplings of scalar fields $s^I$ that are dual to extended chiral primary operators in ${\cal N}=4$ SYM$_4$ are derived by using the covariant equations of motion for type IIB supergravity on $AdS_5\times S^5$. It is shown that despite some expectations if one keeps the structure of the cubic terms untouched, the quartic action obtained contains terms with two and four derivatives. It is shown that the quartic action vanishes on shell in the extremal case, e.g. k_1=k_2+k_3+k_4. Consistency of the truncation of the quartic couplings to the massless multiplet of the ${\cal N}=8$, d=5 supergravity is proven and the explicit values of the couplings are found. It is argued that the consistency of the KK reduction implies non-renormalization of $n$-point functions of $n-1$ operators dual to the fields from the massless multiplet and one operator dual to a field from a massive multiplet.