Quantum Effects of Solitons in the Self-Dual Impurity Model

TL;DR

This paper calculates the quantum vacuum polarization energies of solitons in a self-dual impurity model, revealing how quantum effects influence the preferred separation of kink-antikink pairs.

Contribution

It provides the first computation of quantum corrections to soliton configurations with variable separation in a self-dual impurity model.

Findings

Quantum effects favor specific kink-antikink separations.

VPE is well-defined for all separations due to classical stability.

Quantum corrections modify the classical energy invariance.

Abstract

We compute the vacuum polarization energies (VPE) of solitons in a self-dual impurity model in which the soliton profiles take the shape of a separated kink-antikink pair. Classically the soliton energies are invariant under the change of a continuous parameter that can be interpreted as the kink-antikink separation. This is not the case for the VPE so that quantum effects decide on the energetically most favorable separation. The considered configurations are classically stable so that its quantum fluctuations have only real frequency eigenvalues. Hence, in contrast to the kink-antikink configuration in the $\phi^4$ model, the VPE is well defined for any value of the separation and we gain insight into the quantum corrections to the kink-antikink potential