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

Target space duality symmetries, which acts on Kähler 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 $special$ Kähler, 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.

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