Supersymmetric Nambu$-$Jona-Lasinio Model on ${\cal N}=1/2$ four-dimensional Non(anti)commutative Superspace

TL;DR

This paper develops a four-dimensional supersymmetric Nambu-Jona-Lasinio model with ${ m N}=1/2$ supersymmetry on non(anti)commutative superspace, analyzing its nonperturbative quantum dynamics and dynamical symmetry breaking.

Contribution

It constructs the ${ m N}=1/2$ supersymmetric SNJL model on deformed superspace and investigates its nonperturbative quantum behavior and mass generation mechanisms.

Findings

Demonstrates dynamical symmetry breaking in the deformed superspace

Derives the effective action and solves the gap equation

Shows mass generation via nonperturbative effects

Abstract

We construct the Lagrangian of the ${\cal N}=1$ four-dimensional generalized supersymmetric Nambu$-$Jona-Lasinio (SNJL) model, which has ${\cal N}=1/2$ supersymmetry (SUSY) on non(anti)commutative superspace. A special attention is paid to the examination on the nonperturbative quantum dynamics: The phenomenon of dynamical-symmetry-breaking/mass-generation on the deformed superspace is investigated. The model Lagrangian and the method of SUSY auxiliary fields of composites are examined in terms of component fields. We derive the effective action, examine it, and solve the gap equation for self-consistent mass parameters.