Witten's index and supersymmetric quantum mechanics

Abstract

Criteria for the spontaneous breaking of supersymmetry have been proposed and we examine their range of applicability by evaluating them in some quantum mechanical models. In particular, Str (e−βH) as well as the functional integral expression by Cecotti and Girardello may differ from the integer Δ obtained by zero energy state counting if the spectrum has a continuum part. An attempt to elucidate the difference is made. Also the Nicolai mapping may not have complete range even if the symmetry is unbroken.