Spontaneous Supersymmetry Breaking in Inhomogeneous Supersymmetric Field Theories and BPS Vacua

TL;DR

This paper investigates how inhomogeneous parameters in ${ m N}=1$ supersymmetric field theories can lead to spontaneous supersymmetry breaking or preserve partial supersymmetry, highlighting the role of R-symmetry and inhomogeneous deformations.

Contribution

It analyzes inhomogeneous extensions of ${ m N}=1$ supersymmetric models, showing how inhomogeneous deformations affect supersymmetry and R-symmetry, and discusses conditions for spontaneous supersymmetry breaking.

Findings

Inhomogeneous deformations can preserve half supersymmetry.

Explicit inhomogeneous deformations often break R-symmetry.

Spontaneous supersymmetry breaking is constrained by R-symmetry considerations.

Abstract

We study spontaneous supersymmetry breaking in inhomogeneous extensions of ${\cal N}=1$ supersymmetric field theory models in 4-dimensions. The ${\cal N}=1$ Abelian Higgs model with the inhomogeneous mass parameter and the FI coefficient that are dependent on spatial coordinates, as well as the O'Raifeartaigh model with all its parameters being dependent on spatial coordinates, are studied in detail. In the presence of inhomogeneous parameters, half supersymmetry can be preserved by adding appropriate inhomogeneous deformations to the original Lagrangians. The inhomogeneous deformations often break the R-symmetry explicitly. In cases where the inhomogeneous deformations do not break the R-symmetry explicitly, we demonstrate that spontaneous breaking of the R-symmetry is infeasible. We argue that those models can not be spontaneous supersymmetry breaking models, according to the Nelson-Seiberg argument. We comment on this issue in the context of a generic ${\cal N}=1$ supersymmetric model as well.