The Supersymmetry of Higher-Derivative Supergravity in AdS$_4$ Holography

TL;DR

This paper shows that higher-derivative corrections in 4D gauged supergravity do not alter supersymmetric solutions, and derives a formula for the renormalized on-shell action based on fixed points of a U(1) symmetry.

Contribution

It proves that supersymmetric solutions of the higher-derivative supergravity match those of the two-derivative theory and derives a fixed point formula for the on-shell action.

Findings

Supersymmetric solutions are unchanged by higher-derivative corrections.

A formula for the renormalized on-shell action in terms of fixed points is established.

The on-shell action remains invariant under certain boundary-preserving deformations.

Abstract

An action for the higher-derivative corrections to minimal gauged supergravity in four dimensions has been recently proposed. We demonstrate that the supersymmetric solutions of this model are those of the two-derivative action, and investigate some of their properties. In particular, we prove a formula for the renormalised on-shell action in terms of contributions from fixed points of a $U(1)$ action, and confirm that it is invariant under deformations which preserve the boundary almost contact structure.