1209.0152 (Izu Vaisman)

Towards a double field theory on para-Hermitian manifolds    [PDF]

Izu Vaisman

In a previous paper, we have shown that the geometry of double field theory has a natural interpretation on flat para-Kaehler manifolds. In this paper, we show that the same geometric constructions can be made on any para-Hermitian manifold. The field is interpreted as a compatible (pseudo-)Riemannian metric. The tangent bundle of the manifold has a natural, metric-compatible bracket that extends the C-bracket of double field theory. In the para-Kaehler case this bracket is equal to the sum of the Courant brackets of the two Lagrangian foliations of the manifold. Then, we define a canonical connection and an action of the field that correspond to similar objects of double field theory. Another section is devoted to the Marsden-Weinstein reduction of a para-Hermitian manifold endowed with a double field. Finally, we give examples of double fields on some of the most known para-Hermitian manifolds.

View original: http://arxiv.org/abs/1209.0152