More on Doubled Aspects of Algebroids in Double Field Theory

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.

arXiv commentversion appeared in JMP

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Cited by in corpus (5)

• Double field theory algebroid and curved $L_{\infty }$-algebras
• Gauged Double Field Theory, Current Algebras and Heterotic Sigma Models
• Metric Algebroid and Poisson-Lie T-duality in DFT
• Extended Doubled Structures of Algebroids for Gauged Double Field Theory
• World-volume Effective Theories of Locally Non-geometric Branes