Index theorems and supersymmetry in the soliton sector

Abstract

For arbitrary two-dimensional supersymmetric theories with soliton solutions, we use the Callias-Bott-Seeley trace theorem to calculate the O(h^-) correction to the soliton mass. At the same order the Bogomolny bound is shown, by an explicit computation, to be saturated. The non-vanishing of the mass correction is traced to the existence of supersymmetry violating surface terms in the soliton lagrangian, while the saturation of the Bogomolny bound is a consequence of the absence of spontaneous breaking of N = ½ supersymmetry in a related lagrangian. We argue that this supersymmetry remains unbroken to all orders in perturbation theory. Topological arguments a la Witten are not able to exclude non-perturbative breaking.