Duality versus supersymmetry and compactification.

We study the interplay between T-duality, compactification and supersymmetry. We prove that when the original configuration has unbroken space-time supersymmetries, the dual configuration also does if a special condition is met: the Killing spinors of the original configuration have to be independent on the coordinate which corresponds to the isometry direction of the bosonic fields used for duality. Examples of “losers” (T-duals are not supersymmetric) and “winners” (T-duals are supersymmetric) are given. E-mail address: [email protected] E-mail address: [email protected] E-mail address: [email protected]