3 research outputs found
Twisted C-brackets
We consider the double field formulation of the closed bosonic string theory,
and calculate the Poisson bracket algebra of the symmetry generators governing
both general coordinate and local gauge transformations. Parameters of both of
these symmetries depend on a double coordinate, defined as a direct sum of the
initial and T-dual coordinate. When no antisymmetric field is present, the
-bracket appears as the Lie bracket generalization in a double theory. With
the introduction of the Kalb-Ramond field, the -twisted -bracket appears,
while with the introduction of the non-commutativity parameter, the
-twisted -bracket appears. We present the derivation of these
brackets and comment on their relations to analogous twisted Courant brackets
and T-duality
Courant bracket twisted both by a 2-form
We obtain the Courant bracket twisted simultaneously by a 2-form B and a bi-vector by calculating the Poisson bracket algebra of the symmetry generator in the basis obtained acting with the relevant twisting matrix. It is the extension of the Courant bracket that contains well known Schouten–Nijenhuis and Koszul bracket, as well as some new star brackets. We give interpretation to the star brackets as projections on isotropic subspaces