48 research outputs found
The Algebroid Structure of Double Field Theory
By doubling the target space of a canonical Courant algebroid and
subsequently projecting down to a specific subbundle, we identify the data of
double field theory (DFT) and hence define its algebroid structure. We specify
the properties of the DFT algebroid. We show that one of the Courant algebroid
properties plays the role of the strong constraint in the context of DFT. The
DFT algebroid is a special example when properties of a Courant algebroid are
relaxed in a specific and dependent manner. When otherwise, we uncover
additional structures.Comment: 11 pages; proceedings of "Dualities and Generalized Geometries",
Corfu Summer Institute 2018. v2: typo corrected, reference adde
Generalised Kinematics for Double Field Theory
We formulate a kinematical extension of Double Field Theory on a
-dimensional para-Hermitian manifold where the
metric is supplemented by an almost symplectic two-form
. Together and define an almost bi-Lagrangian structure
which provides a splitting of the tangent bundle
into two Lagrangian subspaces. In this paper a
canonical connection and a corresponding generalised Lie derivative for the
Leibniz algebroid on are constructed. We find integrability
conditions under which the symmetry algebra closes for general and
, even if they are not flat and constant. This formalism thus provides
a generalisation of the kinematical structure of Double Field Theory. We also
show that this formalism allows one to reconcile and unify Double Field Theory
with Generalised Geometry which is thoroughly discussed.Comment: 41 pages, v2: typos corrected, references added, published versio