A Heavy Fermion Can Create a Soliton: A 1+1 Dimensional Example

TL;DR

This paper demonstrates that quantum effects can stabilize a soliton in a 1+1 dimensional scalar-fermion model, where classically no soliton exists, by calculating the exact one-loop fermion contribution to the effective energy.

Contribution

It provides a formalism for exact one-loop fermion energy calculations in scalar backgrounds, showing quantum effects can create stable solitons where none exist classically.

Findings

Quantum effects stabilize a soliton in the model.

The effective energy is finite and unambiguous.

A fermion number one configuration with lower energy than free fermion was found.

Abstract

We show that quantum effects can stabilize a soliton in a model with no soliton at the classical level. The model has a scalar field chirally coupled to a fermion in 1+1 dimensions. We use a formalism that allows us to calculate the exact one loop fermion contribution to the effective energy for a spatially varying scalar background. This energy includes the contribution from counterterms fixed in the perturbative sector of the theory. The resulting energy is therefore finite and unambiguous. A variational search then yields a fermion number one configuration whose energy is below that of a single free fermion.