Calabi-Yau manifolds - motivations and constructions
The possible ways of compactification of the \(E_ 8\otimes E_ 8\) superstring theory to four dimensions are reviewed. The phenomenological need for \(N=1\) supersymmetry is argued (on quite general grounds) to favour the choice of a Calabi-Yau manifold for the compact internal manifold. The massless spectrum after compactification is derived in full detail revealing, beside the usual particles, others that may have great phenomenological impact. The technical aspects of the construction of such manifolds are examined and the methods of calculation of the relevant topological properties are given. A big family of such constructions, giving rise to many new Calabi-Yau manifolds, is presented and its relevance to the search of a phenomenologically acceptable solution is discussed.
scientific article; zbMATH DE number 3971694