Quantum Kinks: Solitons at Strong Coupling

TL;DR

This paper investigates quantum solitons in a (1+1)-dimensional 4 theory with heavy fermions, revealing how strong Yukawa couplings significantly alter soliton properties through fermion loop effects.

Contribution

It introduces a nonperturbative analysis of fermion-induced quantum solitons using a large- expansion and derives a local fermion vacuum energy expression.

Findings

Fermion loop corrections increase kink energy.

Large Yukawa coupling decreases kink size.

Quantum kink energy scales linearly with the coupling g.

Abstract

We examine solitons in theories with heavy fermions. These ``quantum'' solitons differ dramatically from semi-classical (perturbative) solitons because fermion loop effects are important when the Yukawa coupling is strong. We focus on kinks in a $(1+1)$--dimensional $\phi^4$ theory coupled to fermions; a large-$N$ expansion is employed to treat the Yukawa coupling $g$ nonperturbatively. A local expression for the fermion vacuum energy is derived using the WKB approximation for the Dirac eigenvalues. We find that fermion loop corrections increase the energy of the kink and (for large $g$) decrease its size. For large $g$, the energy of the quantum kink is proportional to $g$, and its size scales as $1/g$, unlike the classical kink; we argue that these features are generic to quantum solitons in theories with strong Yukawa couplings. We also discuss the possible instability of fermions to solitons.