Exploring the vicinity of the Bogomol'nyi-Prasad-Sommerfield bound

TL;DR

This paper develops a perturbative method to analyze real scalar field systems near the BPS bound, providing explicit formulas for energy and topological charge, and demonstrating how to lift degeneracies in solutions.

Contribution

It introduces a perturbation approach for scalar field models close to supersymmetric potentials, enabling analytical calculations of energy and charge corrections.

Findings

Derived closed-form expressions for energy and topological charge to first order.

Showed how to lift degeneracy in scalar field solutions.

Applied method to models with one and two scalar fields.

Abstract

We investigate systems of real scalar fields in bidimensional spacetime, dealing with potentials that are small modifications of potentials that admit supersymmetric extensions. The modifications are controlled by a real parameter, which allows implementing a perturbation procedure when such parameter is small. The approach allows obtaining the energy and topological charge in closed forms, up to first order in the parameter. We illustrate the procedure with some examples. In particular, we show how to remove the degeneracy in energy for the one-field and the two-field solutions that appear in a model of two real scalar fields.