Moduli Spaces and Target Space Duality Symmetries in $(0,2)\; Z_N$ Orbifold Theories with Continuous Wilson Lines
G. Lopes Cardoso, D. Luest, T. Mohaupt
TL;DR
This work analyzes the untwisted moduli space of heterotic $(0,2)$ ${Z_N}$ orbifolds with continuous Wilson lines, deriving its local coset structure and constructing explicit Kähler potentials for the ${T_2}$ sector in the $T_6= T_4\oplus T_2$ decomposition. It shows that when the twist has eigenvalues $-1$, holomorphic mixing terms appear among Wilson moduli, leading to mixing between the $T$ and $U$ moduli under target-space dualities. The authors demonstrate that these dualities act as specific Kähler transformations of tree-level supergravity couplings and illustrate the results with detailed constructions for ${Z}_3$ examples and related cosets, including $SO(r,2)$ and $SU(n,1)$ cases. The findings illuminate how moduli associated with Kähler and complex structure deformations fail to factorize in $(0,2)$ compactifications with Wilson lines and set the stage for exploring loop corrections and twisted-sector dynamics. Overall, the paper provides a concrete, Coset-based framework for understanding moduli and dualities in realistic heterotic orbifold compactifications with continuous Wilson lines, with potential implications for gauge symmetry breaking and phenomenology.
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 Kähler potentials associated with the underlying 2-torus $T_2$. We then discuss the transformation properties of these Kähler 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 Kähler 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.