String Theory on Calabi--Yau Manifolds: The Three Generations Case

TL;DR

This paper constructs a consistent string theory on a Calabi--Yau manifold that yields exactly three generations, providing explicit calculations of the spectrum and Yukawa couplings, a key step toward realistic string models.

Contribution

It presents the first complete string theory on the three-generation Calabi--Yau manifold with exact spectrum and Yukawa coupling computations.

Findings

Identification of a unique three-generation Calabi--Yau manifold

Exact calculation of the string spectrum on this manifold

Explicit computation of all Yukawa couplings

Abstract

Recently, string theory on Calabi--Yau manifolds was constructed and was shown to be a fully consistent, space--time supersymmetric string theory. The physically interesting case is the case of three generations. Intriguingly, it appears at the present that there is a unique manifold which gives rise to three generations. We describe in this paper a full fledged string theory on this manifold in which the complete spectrum and all the Yukawa couplings can be computed exactly.