Fermion number fractionization and the Witten index — A new approach

Abstract

States with a fractional fermion number have been discovered in various field theory models. Mathematically, the fermion number is related to the spectral asymmetry of the pertinent Dirac hamiltonian, and several different techniques for its evaluation have been developed. On the other hand, recently it has been established that the Witten index for supersymmetric quantum field theories yields a novel method for the evaluation of an index for a Dirac operator. We show that these two approaches are mathematically equivalent, and we demonstrate how supersymmetry can be used to obtain the fermion number.