Special Geometry and Twisted Moduli in Orbifold Theories with Continuous Wilson Lines

TL;DR

This paper explores how target space duality symmetries in orbifold compactifications are extended to include twisted moduli, revealing their special K"ahler structure and deriving higher order transformation restrictions.

Contribution

It extends the understanding of duality symmetries to include twisted moduli in orbifold theories with continuous Wilson lines, highlighting their special K"ahler geometry.

Findings

Duality transformations are extended to include twisted moduli.

Spaces are shown to be special K"ahler manifolds.

Restrictions on higher order terms in duality transformations are derived.

Abstract

Target space duality symmetries, which acts on K\"ahler and continuous Wilson line moduli, of a ${\bf Z}_N$ ($N\not=2$) 2-dimensional subspace of the moduli space of orbifold compactification are modified to include twisted moduli. These spaces described by the cosets $SU(n,1)\over SU(n)\times U(1)$ are $special$ K\"ahler, a fact which is exploited in deriving the extension of tree level duality transformation to include higher orders of the twisted moduli. Also, restrictions on these higher order terms are derived.