  The interpolation from supersymmetric to non-supersymmetric heterotic
theories is studied, via the Scherk-Schwarz compactification of supersymmetric
6D theories to 4D. A general modular-invariant Scherk-Schwarz deformation is
deduced from the properties of the 6D theories at the endpoints, which
significantly extends previously known examples. This wider class of
non-supersymmetric 4D theories opens up new possibilities for model building.
The full one-loop cosmological constant of such theories is studied as a
function of compactification radius for a number of cases, and the following
interpolating configurations are found: two supersymmetric 6D theories related
by a T-duality transformation, with intermediate 4D maximum or minimum at the
string scale; a non-supersymmetric 6D theory interpolating to a supersymmetric
6D theory, with the 4D theory possibly having an AdS minimum; a "metastable"
non-supersymmetric 6D theory interpolating via a 4D theory to a supersymmetric
6D theory.
