Creation of Bound Half-Fermion Pairs by Solitons

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 $\pm ge^{-gΔ}$, in terms of the Yukawa coupling $g\ll 1$ and the distance $Δ$ 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.