What happens to wavepackets of fermions when scattered by the Maldacena-Ludwig wall?

Abstract

A bstract We study wavepackets of exotic excitations after two-dimensional fermions are scattered by the boundary condition constructed by Maldacena and Ludwig, which turns elementary excitations into exotic fractionally-charged objects. They are of interest in the s-wave approximation of the fermion-monopole scattering in four-dimensional QED and of the multi-channel Kondo effect. Our main result is an explicit expression for the outgoing state of a pair of such particles. We show analytically and numerically that the expectation value 〈 N 〉 of the total number of fermions and anti-fermions diverges when the wavepacket is localized to a point. The energy and charge densities remain localized, and the charge integrated locally around each wavepacket is finite and fractional, as expected from the known action of the boundary condition.