Calabi-Yau supermoduli space, field strength duality and mirror manifolds

Calabi-Yau moduli spaces have a super extension due to their relation to type II superstring compactifications. Supermoduli can be defined as N=2 target space vector-supermultiplets containing both the moduli and their vector field bosonic superpartners. A change of basis in the cohomology vector space corresponds to (modular) duality transformations of target space gvector field strengths. Target space two-forms will take values in the cohomology spaces of Calabi-Yau manifolds, and are therefore related to the Kaehler class and complex structure deformations, which may be relevant for the description of mirror symmetries of (2, 2) superconformal field theories. (orig.)