On Moduli Spaces of CalabiYau Manifolds
Abstract
String theory is a tendimensional theory. If six of those dimensions are compactified on a specific type of manifold called CalabiYau, then at energies that are low compared to the Plank scale, a fourdimensional supergravity theory arises. This manifold possesses a certain number of parameters which span its moduli space. All of the questions raised in this Thesis concern this space. First, the issue of connectedness is addressed. We have proved that the moduli spaces of all CalabiYau manifolds, realized as single hypersurfaces in weighted projective spaces, are connected. This result helps to alleviate some of the discomfort that one feels that the Universe should have to select one of the myriad of CalabiYau compactifications. The complete structure of the moduli spaces of CalabiYau manifolds (and associated LandauGinzburg theories), and hence also of the corresponding lowenergy effective theory that results from (2,2) superstring compactification, may be determined in terms of certain holomorphic functions called periods. The second part of this Thesis addresses this issue. An explicit computation of periods has been given, and it has been pointed out that it is possible to read off from them certain important information related to the mirror manifold. We also develop a homology basis that allows the simple calculation of periods as functions of the complex structure. The final issue addressed here concerns the building blocks for periods, called semiperiods. They are the solutions of the extended PicardFuchs equations before reduction of the order necessary to obtain periods. On the other hand, they are solutions of the integral of a threeform over the chain (instead of a cycle).
 Publication:

Ph.D. Thesis
 Pub Date:
 1996
 Bibcode:
 1996PhDT........32J
 Keywords:

 STRING THEORY;
 COMPACTIFICATION;
 Physics: Elementary Particles and High Energy; Mathematics