Fermions and Supersymmetry Breaking in the Interval

TL;DR

This paper investigates fermions in five-dimensional supersymmetric theories on an interval, revealing how boundary conditions and boundary mass terms influence the mass spectrum and supersymmetry breaking.

Contribution

It introduces a unified parametrization of boundary conditions using complex parameters and analyzes their effects on the fermionic mass spectrum and supersymmetry.

Findings

Boundary conditions are encoded by a complex parameter on the Riemann sphere.

Boundary mass terms determine boundary conditions and bulk equations of motion.

A zero-mode exists for any Scherk-Schwarz parameter, with supersymmetry restored under specific parameter tuning.

Abstract

We study fermions, such as gravitinos and gauginos in supersymmetric theories, propagating in a five-dimensional bulk where the fifth dimensional component is assumed to be an interval. We show that the most general boundary condition at each endpoint of the interval is encoded in a single complex parameter representing a point in the Riemann sphere. Upon introducing a boundary mass term, the variational principle uniquely determines the boundary conditions and the bulk equations of motion. We show the mass spectrum becomes independent from the Scherk-Schwarz parameter for a suitable choice of one of the two boundary conditions. Furthermore, for any value of the Scherk-Schwarz parameter, a zero-mode is present in the mass spectrum and supersymmetry is recovered if the two complex parameters are tuned.