Holomorphic string algebroids

Holomorphic Couplings In Non-Perturbative String Compactifications

In this thesis we present an analysis of several aspects of four-dimensional, non-perturbative N = 1 compactifications of string theory. Our focus is on the study of brane dynamics and their effective physics as encoded in the holomorphic couplings of the low-energy N = 1 effective action, most prominently the superpotential W . The thesis is divided into three parts. In part one we derive the ...

Invariants of Lie algebroids

Several new invariants of Lie algebroids have been discovered recently. We give an overview of these invariants and establish several relationships between them.

Vertex Algebroids I

Omni-lie Algebroids *

A generalized Courant algebroid structure is defined on the direct sum bundle DE ⊕ JE, where DE and JE are the gauge Lie algebroid and the jet bundle of a vector bundle E respectively. Such a structure is called an omni-Lie algebroid since it is reduced to the omni-Lie algebra introduced by A.Weinstein if the base manifold is a point. We prove that any Lie algebroid structure on E is characteri...

DEVELOPMENT IN STRING THEORY

The string theory is a fast moving subject, both physics wise and in the respect of mathematics. In order to keep up with the discipline it is important to move with new ideas which are being stressed. Here I wish to give extracts from new papers of ideas which I have recently found interesting. There are six papers which are involved: I ."Strings formulated directly in 4 dimensions " A. N...