Heavy Fermion Stabilization of Solitons in 1+1 Dimensions

TL;DR

This paper demonstrates that quantum corrections can stabilize static solitons in a (1+1)-dimensional scalar-fermion model that lacks classical solitons, using a renormalized energy functional and phase-shift analysis.

Contribution

It introduces a method to compute and renormalize quantum corrections to stabilize solitons in a model without classical solutions, combining phase-shift techniques with dimensional regularization.

Findings

Identified stable soliton configurations with lower energy than free fermions.

Developed a finite, unambiguous energy functional including quantum corrections.

Established a correspondence between phase shifts and Feynman diagrams for renormalization.

Abstract

We find static solitons stabilized by quantum corrections in a (1+1)-dimensional model with a scalar field chirally coupled to fermions. This model does not support classical solitons. We compute the renormalized energy functional including one-loop quantum corrections. We carry out a variational search for a configuration that minimizes the energy functional. We find a nontrivial configuration with fermion number whose energy is lower than the same number of free fermions quantized about the translationally invariant vacuum. In order to compute the quantum corrections for a given background field we use a phase-shift parameterization of the Casimir energy. We identify orders of the Born series for the phase shift with perturbative Feynman diagrams in order to renormalize the Casimir energy using perturbatively determined counterterms. Generalizing dimensional regularization, we demonstrate that this procedure yields a finite and unambiguous energy functional.