Some aspects of B field and anomalies in string compactifications

Overview & Synopsis

This dissertation discusses some aspects of perturbative and non-perturbative string compactifications. On the perturbative side, we study Heterotic and type II strings compactifications on flat five dimensional manifolds (orbifolds) preserving half of the supersymmetries. By including non-trivial holonomy for Wilson lines. we demonstrate that Heterotic strng compactifications on different classes of internal geometries can be equivalent. Similar equivalence of type II string theories compactifications requires additional B-field configurations. We further discuss these B-field configurations and show how they lead to a perturbative freezing sigularities. On the non-perturbative side, we study (F) M theory compactifications on (elliptic) Calabi-Yau 3-folds and point out the relations between the geometric constraints of elliptic Calabi-Yau 3-folds and recently proposed general consistency conditions for theories of quantum gravity in six dimensions.