All Off-Shell R^2 Invariants in Five Dimensional N=2 Supergravity

TL;DR

This paper constructs all off-shell supersymmetric curvature squared invariants in five-dimensional N=2 supergravity, providing a complete set of supersymmetric completions for various curvature terms and analyzing their effects on solutions.

Contribution

It introduces a comprehensive construction of off-shell supersymmetric R^2 invariants in 5D N=2 supergravity using different Weyl multiplets, completing the set of known curvature squared invariants.

Findings

Constructed minimal off-shell supersymmetric Ricci scalar squared invariant.

Obtained all vector multiplet coupled curvature squared invariants.

Analyzed effects on supersymmetric AdS_5 vacuum and black hole solutions.

Abstract

We construct supersymmetric completions of various curvature squared terms in five dimensional supergravity with eight supercharges. Adopting the dilaton Weyl multiplet, we obtain the minimal off-shell supersymmetric Ricci scalar squared as well as all vector multiplets coupled curvature squared invariants. Since the minimal off-shell supersymmetric Riemann tensor squared and Gauss-Bonnet combination in the dilaton Weyl multiplet have been obtained before, both the minimal off-shell and the vector multiplets coupled curvature squared invariants in the dilation Weyl multiplet are complete. We also constructed an off-shell Ricci scalar squared invariant utilizing the standard Weyl multiplet. The supersymmetric Ricci scalar squared in the standard Weyl multiplet is coupled to n number of vector multiplets by construction, and it deforms the very special geometry. We found that in the supersymmetric AdS_5 vacuum, the very special geometry defined on the moduli space is modified in a simple way. Finally, we study the magnetic string and electric black hole solutions in the presence of supersymmetric Ricci scalar squared.