1992/11/02 by Rolf Schimmrigk, Schimmrigk, Rolf
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Opinion Dynamics and Social Influence #advanced mathematical theories #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9211001
17 pages. Based in part on talks presented at the NATO ARW on Low Dimensional Topology and Quantum Field Theory Cambridge, England, 1992, and the International Workshop on String Theory, Quantum Gravity and the Unification of
arxiv created 1992/11/02 · openalex publication_date 1992/11/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A recently introduced framework for the compactification of supersymmetric string theory involving noncritical manifolds of complex dimension 2k+Dcrit, k≥ 1, is reviewed. These higher dimensional manifolds are spaces with quantized positive Ricci curvature and therefore do not, a priori, describe consistent string vacua. It is nevertheless possible to derive from these manifolds the massless spectra of critical string groundstates. For a subclass of these noncritical theories it is also possible to explicitly construct Calabi--Yau manifolds from the higher dimensional spaces. Thus the new class of theories makes contact with the standard framework of string compactification. This class of manifolds is more general than that of Calabi--Yau manifolds because it contains spaces which correspond to critical string vacua with no Kähler deformations, i.e. no antigenerations, hence providing mirrors of rigid Calabi--Yau manifolds. The constructions reviewed here lead to new insight into the relation between exactly solvable models and their mean field theories on the one hand and Calabi--Yau manifolds on the other, leading, for instance, to a modification of Gepner's conjecture. 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.