Critical superstring vacua from noncritical manifolds: A novel framework for string compactification and mirror symmetry.

Abstract

A new framework is found for the compactification of supersymmetric string theory. It is shown that the massless spectra of critical string vacua with central charge c=3${\mathit{D}}_{\mathrm{crit}}$ can be derived from manifolds of complex dimension ${\mathit{D}}_{\mathrm{crit}}$+2(Q-1),Q\ensuremath{\ge}1, whose first Chern class is quantized in a particular way. This new class is more general than that of Calabi-Yau manifolds because it contains spaces corresponding to vacua with no K\"ahler deformations, i.e., no antigenerations, thus providing mirrors of rigid Calabi-Yau manifolds. The constructions introduced here lead to new insights into the relation between Landau-Ginzburg vacua on the one hand and Calabi-Yau manifolds on the other.