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

TL;DR

This work develops the supersymmetric completion of the mixed gauge-gravitational Chern-Simons term $W\wedge\mathrm{tr}R\wedge R$ in five-dimensional $\mathcal{N}=2$ supergravity using the off-shell superconformal formalism. The authors construct the purely bosonic sector of the higher-derivative $R^2$ term by embedding the Weyl multiplet into a linear multiplet and formulating an invariant action, which also yields corrections to gauge-kinetic and Chern-Simons couplings. They analyze the modified BPS conditions for maximally supersymmetric AdS vacua, showing consistency with the boundary $a$-maximization via AdS/CFT, including the attractor-like relations among the scalar VEVs and gauging parameters. The results provide a controlled framework to study higher-derivative corrections in 5d gauged supergravity and have potential applications to black hole/ring entropy and the landscape of exact supersymmetric solutions.

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.