  We first describe the low energy dynamics of ten dimensional heterotic
supergravity compactified on the smooth, flat 3-manifold ${\mathbb
T^3}/{\mathbb Z_2}$, 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 $\mathbb T^3$, 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 $\text{K3}/\theta$. Our construction gives a novel
CFT description of the semi-classical field theory moduli space. In particular,
the Wilson line parameters in the lattice $I\subset \Gamma_{(19,3)}$ 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.
