String threshold corrections in models with spontaneously broken supersymmetry

We analyse a class of four-dimensional heterotic ground states with N = 2 s pace-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 x T-2. The maximal N = 4 su persymmetry is spontaneously broken to N = 2. The masses of the two massive gravitinos depend on the (T, U) moduli of T-2. We evaluate the one-loop th reshold corrections of gauge and R-2 couplings and we show that they fall i n several universality classes, in contrast to what happens in usual K3 x T -2 compactifications, where the N = 4 supersymmetry is explicitly broken to N = 2, and where a single universality class appears. These universality p roperties 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 T-2 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 x T-2 compactifications, thereby reflecting the existence of s pontaneously 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 rele vance. (C) 1999 Elsevier Science B.V.