Comment on `One Loop Renormalization of Soliton Quantum Mass Corrections in 1+1 Dimensional Scalar Field Theory Models' (Phys. Lett. B542 (2002) 282 [hep-th/0206047])

TL;DR

This paper critiques a previous claim about soliton mass calculations, clarifies the errors in that work, and discusses the quantum stability of a specific scalar field model, suggesting supersymmetry as a potential solution.

Contribution

It refutes a specific incorrect derivation in prior work and analyzes the quantum properties of a scalar field model, proposing supersymmetry to restore soliton stability.

Findings

Previous derivation contained fallacious steps and errors.

The considered model lacks solitons at the quantum level due to vacuum degeneracy lifting.

Supersymmetric extension can restore soliton solutions.

Abstract

We refute the claim that previous works on the one-loop quantum mass of solitons had incorrectly dropped a surface term from a partial integration. Rather, the paper quoted in the title contains a fallacious derivation with two compensating errors. We also remark that the $\phi^2\cos^2\ln(\phi^2)$ model considered in that paper does not have solitons at the quantum level because at two-loop order the degeneracy of the vacua is lifted. This may be remedied, however, by a supersymmetric extension.