String threshold corrections in models with spontaneously broken supersymmetry

We analyse a class of four-dimensional heterotic ground states with N = 2 space-time supersymmetry. From the ten-dimensional perspective, such models can be viewed as compactifications on a six-dimensional manifold with SU(2) holonomy, which is locally but not globally K3 × T2. The maximal N = 4 supersymmetry is spontaneously broken to N = 2. The masses of the two massive gravitinos depend on the (T, U) moduli of T2. We evaluate the one-loop threshold corrections of gauge and R2 couplings and we show that they fall in several universality classes, in contrast to what happens in usual K3 × T2 compactifications, where the N = 4 supersymmetry is explicitly broken to N = 2, and where a single universality class appears. These universality properties follow from the structure of the elliptic genus. The behaviour of the threshold corrections as functions of the moduli is analysed in detail: it is singular across several rational lines of the T2 moduli because of the appearance of extra massless states, and suffers only from logarithmic singularities at large radii. These features differ substantially from the ordinary K3 × T2 compactifications, thereby reflecting the existence of spontaneously broken N = 4 supersymmetry. Although our results are valid in the general framework defined above, we also point out several properties, specific to orbifold constructions, which might be of phenomenological relevance.