Solving the decompactification problem in string theory

We investigate heterotic ground states in four dimensions in which N = 4 supersymmetry is spontaneously broken to N = 2. The N = 4 supersymmetry is restored at a decompactification limit corresponding to m_3/2 → 0. We calculate the full moduli-dependent threshold corrections and confirm that they are suppressed in the decompactification limit, as expected from the restoration of N = 4 supersymmetry. This should be contrasted with the behaviour of the standard N = 2 ground states, where the couplings blow up linearly with the volume of the decompactifying manifold. This mechanism provides a solution to the decompactification problem for the gauge coupling constants. We also discuss how the mechanism can be implemented in ground states with lower supersymmetry.