More on Doubled Aspects of Algebroids in Double Field Theory

TL;DR

This paper explores various algebroid structures in double field theory, revealing their geometric realizations and the conditions under which doubled Poisson structures can be relaxed, advancing the understanding of doubled space-time geometry.

Contribution

It introduces a family of algebroids related to the Drinfel'd double and examines their geometric realization in para-Hermitian manifolds within DFT.

Findings

Doubled algebroids are constructed via Drinfel'd double analogues.

The strong constraint in DFT is necessary for certain structures but can be relaxed.

Doubled structures are related to twisted brackets and group manifolds.

Abstract

We continue to study doubled aspects of algebroid structures equipped with the C-bracket in double field theory (DFT). We find that a family of algebroids, the Vaisman (metric or pre-DFT), the pre- and the ante-Courant algebroids are constructed by the analogue of the Drinfel'd double of Lie algebroid pairs. We examine geometric implementations of these algebroids in the para-Hermitian manifold, which is a realization of the doubled space-time in DFT. We show that the strong constraint in DFT is necessary to realize the doubled and non-trivial Poisson structures but can be relaxed for some algebroids. The doubled structures of twisted brackets and those associated with group manifolds are briefly discussed.