Lectures on generalized complex geometry for physicists

By Paul Koerber. 2010

158 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/52242297ba96a0b8e3c16a191a0a08db0e944402

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Citations in the corpus

β-supergravity: a ten-dimensional theory with non-geometric fluxes, and its geometric framework (2013, unknown): “It finds its origins in Generalized Complex Geometry (GCG) introduced by Hitchin [36] and Gualtieri [37], a mathematical set-up that has been used to study string theory and supergravity with background fluxes [38].”
De Sitter hunting in a classical landscape (2011, background): “where 2κ10 = (2π) l s , Tp = (2π) l s is the D-brane tension, mp = −2p−5 the proportionality between the O-plane and the D-brane tension, and jPD is the actual Poincaré dual to the submanifold (see [32,79,80] for exact definition and conventions for j) that the orientifold wraps.”
Nonperturbative aspects of ABJM theory (2011, result): “We will now confirm this by direct calculation, see [38, 39, 40] for similar considerations.”
Duality Symmetric String and M-Theory (2013, unknown): “3 of the review article [167].”