Symmetry break in a scalar field theory in a $(1 + 1)$-spacetime

TL;DR

This paper investigates symmetry breaking in a relativistic scalar field theory in (1+1) dimensions with periodic potentials, demonstrating spontaneous SUSY breaking through non-zero vacuum expectation values.

Contribution

It introduces a class of periodic potentials in (1+1)D scalar field theory and analyzes the spontaneous symmetry breaking and SUSY breaking mechanisms involved.

Findings

Existence of kink and antikink solutions with topological charges.

Symmetry breaking from zero to non-zero vacuum expectation value.

Spontaneous supersymmetry breaking due to non-zero vev.

Abstract

We consider in this work a relativistic scalar field theory in a $(1+1)$-Minkowski spacetime for a class of periodic potentials. These potentials exhibit solutions known as kinks and antikinks with topological charges, energy density, and mass dependent on the potential's parameters. We break the symmetry from a vacuum expectation value ($vev$) zero for a non-zero $vev$, which means that the supersymmetry (SUSY) has spontaneously broken.