Heterotic Strings on ${\mathbb{T}}^3/{\mathbb{Z}}_2$, Nikulin involutions and M-theory

Abstract

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.

60+12pp

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