Creation of Bound Half-Fermion Pairs by Solitons

TL;DR

This paper explores how topological solitons in 1+1 dimensions can create bound pairs of half-fermions and half-antifermions through their interactions and perturbations, revealing a novel particle creation mechanism.

Contribution

It introduces a new mechanism for creating bound half-fermion pairs via soliton interactions and perturbations, expanding understanding of fermion-soliton dynamics.

Findings

Bound zero modes bifurcate into positive and negative energy levels.

Faraway solitons can induce transitions leading to half-fermion pair creation.

Half-fermion pairs dominate particle production when solitons are well separated.

Abstract

In the presence of topologically nontrivial bosonic field configurations, the fermion number operator may take on fractional eigenvalues, because of the existence of zero-energy fermion modes. The simplest examples of this occur in 1+1 dimensions, with zero modes attached to kink-type solitons. In the presence of a kink-antikink pair, the two associated zero modes bifurcate into positive and negative energy levels with energies $\pm ge^{-g\Delta}$, in terms of the Yukawa coupling $g\ll 1$ and the distance $\Delta$ between the kink and antikink centers. When the kink and antikink are moving, it seems that there could be Landau-Zener-like transitions between these two fermionic modes, which would be interpretable as the creation or annihilation of fermion-antifermion pairs; however, with only two solitons in relative motion, this does not occur. If a third solitary wave is introduced farther away to perturb the kink-antikink system, a movement of the faraway kink can induce transitions between the discrete fermion modes bound to the solitons. These state changes can be interpreted globally as creation or destruction of a novel type of pair: a half-fermion and a half-antifermion. The production of the half-integral pairs will dominate over other particle production channels as long as the solitary waves remain well separated, so that there is a manifold of discrete fermion states whose energies are either zero or exponentially close to zero.