Global Aspects of Doubled Geometry and Pre-rackoid

Abstract

The integration problem of a C-bracket and a Vaisman (metric, pre-DFT) algebroid which are geometric structures of double field theory (DFT) is analyzed. We introduce a notion of a pre-rackoid as a global group-like object for an infinitesimal algebroid structure. We propose that several realizations of pre-rackoid structures. One realization is that elements of a pre-rackoid are defined by cotangent paths along doubled foliations in a para-Hermitian manifold. Another realization is proposed as a formal exponential map of the algebroid of DFT. We show that the pre-rackoid reduces to a rackoid that is the integration of the Courant algebroid when the strong constraint of DFT is imposed. Finally, for a physical application, we exhibit an implementation of the (pre-)rackoid in a three-dimensional topological sigma model.

31 pages, 1 figure, version appeared in JMP

References in corpus (9)

• Double Field Theory
• The gauge algebra of double field theory and Courant brackets
• AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories
• Strings and Branes are Waves
• Non-geometric branes are DFT monopoles
• Generalised Kinematics for Double Field Theory
• Unified picture of non-geometric fluxes and T-duality in double field theory via graded symplectic manifolds
• Unwinding strings in semi-flatland
• A dirty integration of Leibniz algebras

Cited by in corpus (4)

• More on Doubled Aspects of Algebroids in Double Field Theory
• Jacobi-Lie T-plurality
• Towards an extended/higher correspondence -- Generalised geometry, bundle gerbes and global Double Field Theory
• Extended Doubled Structures of Algebroids for Gauged Double Field Theory