Calabi-Yau manifolds with $B$-fields

TL;DR

This paper introduces generalized geometry, focusing on structures acted upon by diffeomorphisms and B-fields, with examples from Calabi-Yau manifolds and applications in string theory.

Contribution

It provides an introduction to generalized geometry, illustrating how B-fields extend traditional structures and exploring their relevance to Calabi-Yau manifolds and string theory.

Findings

Generalized geometry incorporates B-fields into geometric structures.

Examples demonstrate how Calabi-Yau manifolds fit into generalized geometry.

Applications to string theory highlight the physical relevance of these structures.

Abstract

In recent work N. Hitchin introduced the concept of "generalised geometry". The key feature of generalised structures is that that they can be acted on by both diffeomorphisms and 2-forms, the so-called $B$-fields. In this lecture, we give a basic introduction and explain some of the fundamental ideas. Further, we discuss some examples of generalised geometries starting from the usual notion of a Calabi-Yau manifold, as well as applications to string theory.