Nonlocal N=1 Supersymmetry

TL;DR

This paper develops four-dimensional $ abla=1$ supersymmetric nonlocal theories, analyzing higher derivative extensions, auxiliary field conditions, and the impact on supersymmetry breaking, including modifications to supertrace formulas.

Contribution

It introduces a framework for constructing $ abla=1$ supersymmetric nonlocal theories, detailing conditions for auxiliary fields and ghost-free dynamical scalars and fermions.

Findings

Auxiliary fields can remain non-dynamical under specific conditions.

Nonlocal effects significantly modify supertrace (mass) formulas.

Theories avoid ghost degrees of freedom with appropriate higher derivative terms.

Abstract

We construct $\mathcal{N}=1$ supersymmetric nonlocal theories in four dimension. We discuss higher derivative extensions of chiral and vector superfields, and write down generic forms of K\"ahler potential and superpotential up to quadratic order. We derive the condition in which an auxiliary field remains non-dynamical, and the dynamical scalars and fermions are free from the ghost degrees of freedom. We also investigate the nonlocal effects on the supersymmetry breaking and find that supertrace (mass) formula is significantly modified even at the tree level.