Implications of Lorentz symmetry violation on a 5D supersymmetric model

TL;DR

This paper investigates how Lorentz symmetry violation in a 5D supersymmetric model affects supersymmetry after compactification, revealing conditions under which supersymmetry can be preserved or broken in the effective 4D theory.

Contribution

It demonstrates that supersymmetry can be restored in 5D models with Lorentz violation through a deformation of transformations, and explores the impact of parity preservation on supersymmetric KK models.

Findings

Supersymmetry can be restored in 5D Lorentz violating models via deformation.

Lorentz violating operators that break parity lead to supersymmetry breaking in 4D.

Parity-preserving models maintain well-defined supersymmetric KK spectra.

Abstract

Field models with $n$ extra spatial dimensions have a larger $SO(1,3+n)$ Lorentz symmetry which is broken down to the standard $SO(1,3)$ four dimensional one by the compactification process. By considering Lorentz violating operators in a $5D$ supersymmetric Wess-Zumino mo\-del, which otherwise conserve the standard four dimensional Poincare invariance, we show that supersymmetry can be restored upon a simple deformation of the supersymmetric transformations. However, supersymmetry is not preserved in the effective $4D$ theory that arises after compactification when the $5D$ Lorentz violating operators do not preserve $Z_2: y\rightarrow -y$ bulk parity. Our mechanism unveils a possible connection among Lorentz violation and the Scherk-Schwarz mechanism. We also show that parity preserving models, on the other hand, do provide well defined supersymmetric KK models.