Spinorial geometry, off-shell Killing spinor identities and higher derivative 5D supergravities

TL;DR

This paper derives Killing spinor identities for five-dimensional off-shell supergravities, enabling analysis of supersymmetric solutions including higher derivative corrections, without relying on specific actions.

Contribution

It provides explicit Killing spinor identities for 5D $ ext{N}=2$ supergravities with matter, applicable to arbitrary higher derivative extensions, using spinorial geometry techniques.

Findings

Derived Killing spinor identities for off-shell supergravities.

Analyzed time-like class of solutions with four-derivative corrections.

Discussed maximally supersymmetric solutions in the off-shell framework.

Abstract

Killing spinor identities relate components of equations of motion to each other for supersymmetric backgrounds. The only input required is the field content and the supersymmetry transformations of the fields, as long as an on-shell supersymmetrization of the action without additional fields exists. If we consider off-shell supersymmetry it is clear that the same relations will occur between components of the equations of motion independently of the specific action considered, in particular the Killing spinor identities can be derived for arbitrary, including higher derivative, supergravities, with a specified matter content. We give the Killing spinor identities for five-dimensional $\mathcal{N}=2$ ungauged supergravities coupled to Abelian vector multiplets, and then using spinorial geometry techniques so that we have explicit representatives for the spinors, we discuss the particular case of the time-like class of solutions to theories with perturbative corrections at the four derivative level. We also discuss the maximally supersymmetric solutions in the general off-shell case.