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arXiv · 1209.0152

Towards a double field theory on para-Hermitian manifolds

Izu Vaisman
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Abstract

In a previous paper, we have shown that the geometry of double field theory has a natural interpretation on flat para-K\"ahler 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-K\"ahler 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 in double field theory on para-Hermitian manifolds. Finally, we give examples of fields on some well-known para-Hermitian manifolds.

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Izu Vaisman. 2012-09-02. Towards a double field theory on para-Hermitian manifolds. https://doi.org/10.1063/1.4848777

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