Moduli Spaces and Target Space Duality Symmetries in $(0,2)\; Z_N$ Orbifold Theories with Continuous Wilson Lines

TL;DR

This paper analyzes the structure of the moduli space in heterotic $(0,2)$ orbifold compactifications with Wilson lines, focusing on the Kähler potentials and their transformation under target space dualities, revealing mixing of moduli.

Contribution

It explicitly constructs the Kähler potentials for certain orbifold models and studies their transformation properties, highlighting new mixing effects of moduli under dualities.

Findings

Kähler potentials are explicitly constructed for specific orbifold cases.

Target space modular transformations induce mixing of $T$ and $U$ moduli.

Holomorphic terms appear in the Kähler potential for certain twists.

Abstract

We present the coset structure of the untwisted moduli space of heterotic $(0,2) \; Z_N$ orbifold compactifications with continuous Wilson lines. For the cases where the internal 6-torus $T_6$ is given by the direct sum $T_4 \oplus T_2$, we explicitly construct the K\"{a}hler potentials associated with the underlying 2-torus $T_2$. We then discuss the transformation properties of these K\"{a}hler potentials under target space modular symmetries. For the case where the $Z_N$ twist possesses eigenvalues of $-1$, we find that holomorphic terms occur in the K\"{a}hler potential describing the mixing of complex Wilson moduli. As a consequence, the associated $T$ and $U$ moduli are also shown to mix under target space modular transformations.