Lectures on Generalized Complex Geometry for Physicists

Details Lectures on Generalized Complex Geometry for Physicists Lectures on Generalized Complex Geometry for Physicists

2010-06-08

arxiv.org/abs/1006.1536v2

Fortsch.Phys.59:169-242,2011

Physics

High Energy Physics

High Energy Physics - Theory

94 pages, 4 figures, 5 tables, lectures Sogang University August 2007 and Modave Summer School September 2008, v2: references

Scientific paper

10.1002/prop.201000083

In these lectures we review Generalized Complex Geometry and discuss two main applications to string theory: the description of supersymmetric flux compactifications and the supersymmetric embedding of D-branes. We start by reviewing G-structures, and in particular SU(3)-structure and its torsion classes, before extending to Generalized Complex Geometry. We then discuss the supersymmetry conditions of type II supergravity in terms of differential conditions on pure spinors, and finally introduce generalized calibrations to describe D-branes. As examples we discuss in some detail AdS4 compactifications, which play a role as the geometric duals in the AdS4/CFT3-correspondence.

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