Supersymmetric Completion of an R^2 Term in Five-Dimensional Supergravity

TL;DR

This paper constructs the supersymmetric completion of an R^2 higher derivative term in five-dimensional supergravity using superconformal methods, and relates it to boundary CFT conditions via AdS/CFT.

Contribution

It explicitly derives the bosonic terms connected to the mixed gauge-gravitational Chern-Simons term in 5D supergravity and links the supersymmetric AdS vacuum condition to 4D a-maximization.

Findings

Derived the supersymmetric completion of the R^2 term.

Established the vacuum condition matches 4D a-maximization.

Connected supergravity corrections to boundary CFT predictions.

Abstract

We analyze the structure of a particular higher derivative correction of five-dimensional ungauged and gauged supergravity with eight supercharges. Specifically, we determine all the purely bosonic terms which are connected by the supersymmetry transformation to the mixed gauge-gravitational Chern-Simons term, W wedge tr R wedge R. Our construction utilizes the superconformal formulation of supergravity. As an application, we determine the condition for the supersymmetric anti-de Sitter vacuum with this term. We check that it gives precisely the same condition as the a-maximization in four-dimensional superconformal field theory on the boundary, as predicted by the AdS/CFT correspondence.