On Five-dimensional Superspaces

TL;DR

This paper develops a manifestly supersymmetric 5D superspace formalism with eight supercharges, simplifying calculations and enabling new model building in five-dimensional supersymmetric theories.

Contribution

It introduces a new supergraph-compatible formalism for 5D supersymmetric theories that maintains 4D N=1 supersymmetry manifestly, facilitating higher-loop calculations and model construction.

Findings

Formulation of a 5D superspace with manifest supersymmetry.

Derivation of rules to reduce 5D actions to hybrid 4D N=1 form.

Construction of off-shell 5D supersymmetric nonlinear sigma-models.

Abstract

Recent one-loop calculations of certain supergravity-mediated quantum corrections in supersymmetric brane-world models employ either the component formulation (hep-th/0305184) or the superfield formalism with only half of the bulk supersymmetry manifestly realized (hep-th/0305169 and hep-th/0411216). There are reasons to expect, however, that 5D supergraphs provide a more efficient setup to deal with these and more involved (in particular, higher-loop) calculations. As a first step toward elaborating such supergraph techniques, we develop in this letter a manifestly supersymmetric formulation for 5D globally supersymmetric theories with eight supercharges. Simple rules are given to reduce 5D superspace actions to a hybrid form which keeps manifest only the 4D, N=1 Poincare supersymmetry. (Previously, such hybrid actions were carefully worked out by rewriting the component actions in terms of simple superfields). To demonstrate the power of this formalism for model building applications, two families of off-shell supersymmetric nonlinear sigma-models in five dimensions are presented (including those with cotangent bundles of Kahler manifolds as target spaces). We elaborate, trying to make our presentation maximally clear and self-contained, on the techniques of 5D harmonic and projective superspaces used at some stages in this letter.