Non-Local Deformation of a Supersymmetric Field Theory

TL;DR

This paper investigates a supersymmetric field theory deformed by generalized uncertainty principle and Lifshitz scaling, revealing non-local fractional derivatives and partial supersymmetry preservation.

Contribution

It introduces a method to construct a deformed N=1 supersymmetric theory using harmonic extension, highlighting supersymmetry breaking with interactions.

Findings

Deformed theory contains non-local fractional derivatives.

Supersymmetry preserved only in free theory, broken by interactions.

Harmonic extension used to construct the deformed supersymmetric model.

Abstract

In this paper, we will analyse a supersymmetric field theory deformed by generalized uncertainty principle and Lifshitz scaling. It will be observed that this deformed supersymmetric field theory contains non-local fractional derivative terms. In order to construct such deformed N=1 supersymmetric theory, a harmonic extension of functions will be used. However, the supersymmetry will be only preserved for a free theory and will be broken by the inclusion of interaction terms.