In this review we study BPS D-branes on Calabi-Yau threefolds. Such D-branes naturally
divide into two sets called A-branes and B-branes which are most easily understood from …

We reconsider the role that bundle gerbes play in the formulation of the WZW model on
closed and open surfaces. In particular, we show how an analysis of bundle gerbes on …

Generalized complex geometry encompasses complex and symplectic geometry as its
extremal special cases. We explore the basic properties of this geometry, including its …

This thorough and detailed exposition is the result of an intensive month-long course on
mirror symmetry sponsored by the Clay Mathematics Institute. It develops mirror symmetry …

A geometrical structure on even‐dimensional manifolds is defined which generalizes the
notion of a Calabi–Yau manifold and also a symplectic manifold. Such structures are of …

A bstract We reformulate ten-dimensional type II supergravity as a generalised geometrical
analogue of Einstein gravity, defined by an O (9, 1)× O (1, 9)⊂ O (10, 10)×\({\mathbb …

We show that generalised geometry gives a unified description of bosonic eleven-
dimensional supergravity restricted to a d-dimensional manifold for all d≤ 7. The theory is …

A bstract We reformulate eleven-dimensional supergravity, including fermions, in terms of
generalised geometry, for spacetimes that are warped products of Minkowski space with a d …

Among the major mathematical approaches to mirror symmetry are those of Batyrev-Borisov
and Strominger-Yau-Zaslow (SYZ). The first is explicit and amenable to computation but is …

The N= 1 effective action for generic type IIA Calabi–Yau orientifolds in the presence of
background fluxes is computed from a Kaluza–Klein reduction. The Kähler potential, the …