Twisting Toroidally Compactified Heterotic Strings with Enlarged Symmetry Groups

In toroidal compactification of string theory, enlarged symmetry groups arise at special radii of the compactified dimensions. Here an orbifold-like construction is considered in which the degrees of freedom describing the compact spatial dimensions are twisted by symmetries which exist only for special values of the radius. Constraints on the possible twists arising from the requirements of worldsheet supersymmetry and modular invariance are described, and some simple examples are given. One motivation for this work is that in twisting by a symmetry which exists only at a special value of the radius, one of the dilaton-like fields can acquire a mass, since the radius of the compact space is fixed.