Rigid Supersymmetry from Conformal Supergravity in Five Dimensions

TL;DR

This paper investigates the conditions under which five-dimensional conformal supergravity backgrounds admit rigid supersymmetry, linking the existence of conformal Killing vectors and specific geometric structures to the presence of kinetic terms in the action.

Contribution

It establishes the precise geometric conditions for rigid supersymmetry in 5d conformal supergravity and explores when these backgrounds support kinetic Yang-Mills terms.

Findings

Existence of conformal Killing vectors is necessary and sufficient for rigid supersymmetry.

When an $SU(2)$ curvature becomes abelian, backgrounds define a transversally holomorphic foliation.

Kinetic Yang-Mills terms require the conformal Killing vector to be Killing.

Abstract

We study the rigid limit of 5d conformal supergravity with minimal supersymmetry on Riemannian manifolds. The necessary and sufficient condition for the existence of a solution is the existence of a conformal Killing vector. Whenever a certain $SU(2)$ curvature becomes abelian the backgrounds define a transversally holomorphic foliation. Subsequently we turn to the question under which circumstances these backgrounds admit a kinetic Yang-Mills term in the action of a vector multiplet. Here we find that the conformal Killing vector has to be Killing. We supplement the discussion with various appendices.