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

A new framework is found for the compactification of supersymmetric string theory. It is shown that the massless spectra of Calabi–Yau manifolds of complex dimension Dcrit can be derived from noncritical manifolds of complex dimension 2k + Dcrit, k ≥ 0. These higher dimensional manifolds are spaces whose nonzero Ricci curvature is quantized in a particular way. This class is more general than that of Calabi–Yau manifolds because it contains spaces that correspond to critical string vacua with no Kähler 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 exactly solvable models and their mean field theories on the one hand and Calabi–Yau manifolds on the other. They also raise fundamental questions about the Kaluza–Klein concept of string compactification, in particular regarding the rôle played by the dimension of the internal theories. PACS numbers: 11.17.+y, 11.10Kk, 02.40.+m, 04.60.+n Email address: [email protected]