What, exactly, is a Calabi-Yau manifold?
String theory describes one of the smallest things you can possibly imagine — six-dimensional geometric spaces that may be more than a trillion times smaller than an electron — that could be one of the defining features of our universe. The story of these spaces, can be explained by what physicists call “Calabi-Yau manifolds,” Superstring theory is a unified theory for all the forces of nature including quantum gravity. In superstring theory, the fundamental building block is an extended object, namely a string, whose vibrations would give rise to the particles encountered in nature. The constraints for the consistency of such a theory are extremely stringent. They require in particular that the theory takes place in a 10-dimensional space-time. To make contact with our 4-dimensional world, it is expected that the 10-dimensional space-time of string theory is locally the product M 4 ×X of a 4-dimensional Minkowski space M 3,1 with a 6-dimensional space X . The 6-dimensional space X ...