A supersymmetric exotic field theory in (1+1) dimensions. One loop soliton quantum mass corrections

TL;DR

This paper calculates one-loop quantum corrections to soliton masses in a supersymmetric (1+1)D field theory with a complex potential, revealing unexpected divergence behavior at certain parameters.

Contribution

It provides a finite, unambiguous formula for one-loop soliton mass corrections in a novel supersymmetric model, extending previous results to a new potential.

Findings

Quantum corrections match known models like sine-Gordon and φ^4.

Supersymmetry can worsen ultraviolet divergences in this model.

Finite correction formulas are derived for the soliton mass.

Abstract

We consider one loop quantum corrections to soliton mass for the ${\cal N}=1$ supersymmetric extension of the (1+1)-dimensional scalar field theory with the potential $U(\phi) = \phi^2 \cos^2\left(\ln \phi^2\right)$. First, we compute the one loop quantum soliton mass correction of the bosonic sector. To do that, we regularize implicitly such quantity by subtracting and adding its corresponding tadpole graph contribution, and use the renormalization prescription that the added term vanishes with the corresponding counterterms. As a result we get a finite unambiguous formula for the soliton quantum mass corrections up to one loop order. Afterwards, the computation for the supersymmetric case is extended straightforwardly and we obtain for the one loop quantum correction of the SUSY kink mass the expected value previously derived for the SUSY sine-Gordon and $\phi^4$ models. However, we also have found that for a particular value of the parameters, contrary to what was expected, the introduction of supersymmetry in this model worsens ultraviolet divergences rather than improving them.