David Andriot (Paris, LPTHE)
Solvmanifolds, in particular nilmanifolds, commonly known as twisted tori,
provide several examples of internal manifolds in flux compactifications
towards de Sitter, Minkowski or Anti de Sitter. The properties of these
manifolds, their relation to the six-dimensional torus, and the string
vacua obtained on them are the main interests of this talk.
We will first present some properties of these manifolds. We will give a
generic construction of their Maurer-Cartan forms out of the
six-dimensional torus, via a transformation called the twist. This
transformation actually encodes most the properties of these manifolds, in
particular their compactness.
We will then describe several Minkowski flux backgrounds of type II
supergravity obtained on these manifolds. Thanks to the generalized
complex geometry approach, we will show that one can obtain those
solutions from solutions on the torus, via the twist transformation. The
latter is then able to relate backgrounds which are not T-duals. Finally,
we will apply this twist transformation technique to relate
Kahler/non-Kahler solutions of the heterotic string.
This talk is based on a work with Enrico Goi, Ruben Minasian and Michela
Petrini, 0903.0633 and to appear soon.
Arnold Sommerfeld Center