Fractional topological charge, torons and breaking of discrete chiral symmetry in the supersymmetric O(3) σ model

A novel class of self-dual solutions in the O(3)σ model with a half topological charge Q=1/2 is considered. The contribution of the corresponding fluctuations to (ψ-barψ) is calculated. The result is finite, and this indicates that chiral symmetry is broken spontaneously. Various possible ways of describing such fluctuations are considered, e.g. analytic continuation to complex space and the alternative description on orbifolds