Lectures on Generalized Complex Geometry for Physicists
arXiv:1006.1536 · doi:10.1002/prop.201000083
Abstract
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.
94 pages, 4 figures, 5 tables, lectures Sogang University August 2007 and Modave Summer School September 2008, v2: references added
References in corpus (49)
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- Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
- Flux Compactification
- Generalised Geometry for M-Theory
- Doubled Geometry and T-Folds
- Lectures on Gauged Supergravity and Flux Compactifications
- Generalized N=1 Orientifold Compactifications and the Hitchin functionals
- Moduli spaces of Chern-Simons quiver gauge theories and AdS_4/CFT_3
- Physics of String Flux Compactifications
- The effective theory of type IIA AdS4 compactifications on nilmanifolds and cosets
- Generalized non-supersymmetric flux vacua
- On Slow-roll Moduli Inflation in Massive IIA Supergravity with Metric Fluxes
- On the Cosmology of Type IIA Compactifications on SU(3)-structure Manifolds
- ABJM with Flavors and FQHE
- Minimal Simple de Sitter Solutions
- Type IIA AdS4 compactifications on cosets, interpolations and domain walls
- Gauged Supergravities from Twisted Doubled Tori and Non-Geometric String Backgrounds
- New supersymmetric AdS4 type II vacua
- Deformations of calibrated D-branes in flux generalized complex manifolds
- Supersymmetry breaking branes on solvmanifolds and de Sitter vacua in string theory
- Reformulating Supersymmetry with a Generalized Dolbeault Operator
- New string vacua from twistor spaces
- Effective actions and N=1 vacuum conditions from SU(3) x SU(3) compactifications
- Massive type IIA string theory cannot be strongly coupled
- U-dual fluxes and Generalized Geometry
- Perturbing gauge/gravity duals by a Romans mass
- Superconformal Chern-Simons Theories and the Squashed Seven Sphere
- Nearly Kaehler Reduction
- Generalized geometry and the Hodge decomposition
- On the supergravity formulation of mirror symmetry in generalized Calabi-Yau manifolds
- T-duality with H-flux: non-commutativity, T-folds and G x G structure
- Classes of AdS4 type IIA/IIB compactifications with SU(3)xSU(3) structure
- Gravity duals to deformed SYM theories and Generalized Complex Geometry
- N=2 solutions of massive type IIA and their Chern-Simons duals
- D-brane networks in flux vacua, generalized cycles and calibrations
- Coisotropic D8-branes and Model-building
- Generalized Kaehler Potentials from Supergravity
- NS-NS fluxes in Hitchin's generalized geometry
- On Deformations of Generalized Complex Structures: the Generalized Calabi-Yau Case
- Domain walls from ten dimensions
- The biHermitian topological sigma model
- No-scale supersymmetry breaking vacua and soft terms with torsion
- Linearizing Generalized Kahler Geometry
- Generalized Calabi-Yau structures and mirror symmetry
- Type II compactifications on manifolds with SU(2) x SU(2) structure
- Potentials for Light Moduli in Supergravity and String Theory
- An N=2 worldsheet approach to D-branes in bihermitian geometries: I. Chiral and twisted chiral fields
- An N=2 worldsheet approach to D-branes in bihermitian geometries: II. The general case
- Coisotropic D-branes on AdS4 x CP3 and massive deformations