|XXXIV Workshop on Geometric Methods in Physics||28.06-4.07.2015|
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Star products on graded manifolds and deformations of Courant algebroids from string theory
Deformations of Courant algebroids are of interest in both, string
theory and mathematics.
It was realized by Roytenberg, that Lie bialgebroids and their
associated Courant algebroids can be characterized by a homological
vector field on the cotangent bundle of the parity reversed version of
the underlying Lie algebroid. This lead to the introduction of the
Drinfel'd double of a Lie bialgebroid.
In a similar way, we show that the so-called C-bracket, a bi-linear
operation governing the gauge algebra of double field theory, can be
characterized by the Poisson structure on the Drinfel'd double of the
Using this result, we are able to apply a graded version of the
Moyal-Weyl star product to compute the first order deformation of the
C-bracket. Remarkably, these coincide with the first order correction
in the string coupling parameter found recently in string theory.