Topological solitons in a vacuumless system

TL;DR

This paper explores topological solitons in a two-dimensional scalar field model with a potential lacking vacuum states, revealing BPS solutions with unique energy profiles and zero modes, expanding understanding of non-vacuum topological structures.

Contribution

It introduces a novel scalar field model with a positive semi-definite potential without vacuum states, demonstrating BPS topological solutions with Lorentzian energy density.

Findings

BPS solutions differ from standard kinks.

Solutions support bosonic and fermionic zero modes.

Energy density follows a Lorentzian law.

Abstract

We investigate a model for a real scalar field in bidimensional space-time, described in terms of a positive semi-definite potential that presents no vacuum state. The system presents topological solutions of the BPS type, with energy density that follows a Lorentzian law. These BPS solutions differ from the standard $\tanh$-type kink, but they also support bosonic and fermionic zero modes.