Noncommutativity and nonassociativity of type II superstring with coordinate dependent RR field - the general case

In this paper we consider non-commutativity that arises from T-duality of bosonic coordinates of type II superstring in presence of coordinate dependent Ramond-Ramond field. Action with such choice of the background fields is not translational invariant. Consequently, we will employ generalization of Buscher procedure that can be applied to cases that have coordinate dependent fields and that do not possess translational isometry. Bosonic part of newly obtained T-dual theory is non-local and defined in non-geometric double space spanned by Lagrange multipliers y(mu) and double coordinate increment V-mu. We will apply Buscher procedure once more on T-dual theory to check if original theory can be salvaged. Finally, we will use T-dual transformation laws along with Poisson brackets of original theory to derive Poisson bracket structure of T-dual theory.

Automated summary

In this paper, we investigate the non-commutativity arising from T-duality of bosonic coordinates in type II superstring with coordinate dependent Ramond-Ramond field. We consider the generalization of Buscher procedure to handle cases with coordinate dependent fields and without translational isometry. The obtained T-dual theory has a non-local bosonic part defined in a non-geometric double space. We apply Buscher procedure again to examine whether the original theory can be salvaged and use T-dual transformation laws and Poisson brackets to derive the Poisson bracket structure of the T-dual theory.