Parity Conservation in Supersymmetric Vector-Like Theories

TL;DR

This paper demonstrates that parity symmetry is preserved in vector-like supersymmetric theories, including cases with supersymmetry breaking via gluino masses, based on fermionic path-integral methods.

Contribution

It extends the Vafa-Witten fermionic path-integral approach to show parity conservation in supersymmetric theories with massive quarks and broken supersymmetry.

Findings

Parity is conserved in supersymmetric QCD with massive quarks.

Parity remains conserved even with gluino mass-induced supersymmetry breaking.

The result holds when considering only bosonic parity-breaking observables.

Abstract

We show that parity is conserved in vector-like supersymmetric theories, such as supersymmetric QCD with massive quarks with no cubic couplings among chiral multiplets, based on fermionic path-integrals, originally developed by Vafa and Witten. We also look into the effect of supersymmetric breaking through gluino masses, and see that the parity-conservation is intact also in this case. Our conclusion is valid, when only bosonic parity-breaking observable terms are considered in path-integrals like the original Vafa-Witten formulation.