Heterotic strings on T3/Z2, Nikulin involutions and M-theory

We first describe the low energy dynamics of ten dimensional heterotic supergravity compactified on the smooth, flat 3-manifold T-3/Z(2), without supersymmetry, and explain how it arises from flat heterotic gauge fields. The semi-classical theory has both Coulomb and Higgs branches of non-supersymmetric vacua. We then give an exact worldsheet description as asymmetric orbifolds of T-3, where the orbifold generator involves a Nikulin non-symplectic involution theta of the even self-dual lattice Gamma((19,3)). Along the way we briefly compare our findings with M-theory on K3/theta. Our construction gives a novel CFT description of the semi-classical field theory moduli space. In particular, the Wilson line parameters in the lattice I subset of Gamma((19,3)) of signature (19 - s, 1) which is invariant under theta, and in its orthogonal complement N, correspond respectively to Coulomb and Higgs branch moduli. There is a rich pattern of transitions amongst Higgs and Coulomb branches which we describe using the worldsheet theory.