Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1992-07-22
Phys.Rev. D46 (1992) 5487-5496
Physics
High Energy Physics
High Energy Physics - Theory
21 pp. + 2 figs., phyzzx, JHU-TIPAC-920014
Scientific paper
10.1103/PhysRevD.46.5487
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.
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