Searching for Quantum Solitons in a 3+1 Dimensional Chiral Yukawa Model

TL;DR

This paper investigates the existence of quantum-stabilized solitons in a 3+1 dimensional Yukawa model with heavy fermions, incorporating exact one-loop quantum corrections and variational methods.

Contribution

It introduces a method to compute quantum corrections using phase shifts and develops a simplified approach for higher-order Born series terms in a 3+1D Yukawa model.

Findings

Marginally bound configurations at large Yukawa coupling.

Quantum corrections influence soliton stability.

Methodology for renormalized energy functional calculation.

Abstract

We search for static solitons stabilized by heavy fermions in a 3+1 dimensional Yukawa model. We compute the renormalized energy functional, including the exact one-loop quantum corrections, and perform a variational search for configurations that minimize the energy for a fixed fermion number. We compute the quantum corrections using a phase shift parameterization, in which we renormalize by identifying orders of the Born series with corresponding Feynman diagrams. For higher-order terms in the Born series, we develop a simplified calculational method. When applicable, we use the derivative expansion to check our results. We observe marginally bound configurations at large Yukawa coupling, and discuss their interpretation as soliton solutions subject to general limitations of the model.