Five-dimensional vector multiplets in arbitrary signature

TL;DR

This paper develops a formalism for constructing supersymmetric theories in arbitrary space-time signatures, focusing on five-dimensional vector multiplets, and explores the implications of different signatures on R-symmetry and kinetic terms.

Contribution

It introduces a complex supersymmetry algebra framework that generalizes spinor representations and constructs off-shell supersymmetry transformations for 5D vector multiplets in any signature.

Findings

R-symmetry groups are SO(2), SO(1,1), SU(2), or SU(1,1) depending on the spinor structure.

In Euclidean signature, scalar and vector kinetic terms differ by a sign.

The Euclidean supersymmetry algebra implies an inevitable sign flip in kinetic terms.

Abstract

We start developing a formalism which allows to construct supersymmetric theories systematically across space-time signatures. Our construction uses a complex form of the supersymmetry algebra, which is obtained by doubling the spinor representation. This allows one to partially disentangle the Lorentz and R-symmetry group and generalizes symplectic Majorana spinors. For the case where the spinor representation is complex-irreducible, the R-symmetry only acts on an internal multiplicity space, and we show that the connected groups which occur are SO(2), SO(1,1), SU(2) and SU(1,1). As an application we construct the off-shell supersymmetry transformations and supersymmetric Lagrangians for five-dimensional vector multiplets in arbitrary signature (t,s). In this case the R-symmetry groups are SU(2) or SU(1, 1), depending on whether the spinor representation carries a quaternionic or para-quaternionic structure. In Euclidean signature the scalar and vector kinetic terms differ by a relative sign, which is consistent with previous results in the literature and shows that this sign flip is an inevitable consequence of the Euclidean supersymmetry algebra.