Mirror Symmetry in Generalized Calabi–Yau Compactifications

We discuss mirror symmetry in generalized Calabi–Yau compactifications of type II string theories with background NS fluxes. Starting from type IIB compactified on Calabi– Yau threefolds with NS three-form flux we show that the mirror type IIA theory arises from a purely geometrical compactification on a different class of six-manifolds. These mirror manifolds have SU(3) structure and are termed half-flat; they are neither complex nor Ricci-flat and their holonomy group is no longer SU (3). We show that type IIA appropriately compactified on such manifolds gives the correct mirror-symmetric lowenergy effective action. November 2002 Work supported by: DFG – The German Science Foundation, GIF – the German–Israeli Foundation for Scientific Research, European RTN Program HPRN-CT-2000-00148 and the DAAD – the German Academic Exchange Service, the CNRS – the French Center for National Scientific Research and the Royal Society, UK. On leave from IFIN-HH Bucharest