2015/11/12 by Andreas Deser, Deser, Andreas
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1511.03929
openalex publication_date 2015/11/12 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
Originally proposed as an O(d,d)-invariant formulation of classical closed string theory, double field theory (DFT) offers a rich source of mathematical structures. Most prominently, its gauge algebra is determined by the so-called C-bracket, a generalization of the Courant bracket of generalized geometry, in the sense that it reduces to the latter by restricting the theory to solutions of a "strong constraint". Recently, infinitesimal deformations of these structures in the string sigma model coupling α' were found. In this short contribution, we review constructing the Drinfel'd double of a Lie bialgebroid and offer how this can be applied to reproduce the C-bracket of DFT in terms of Poisson brackets. As a consequence, we are able to explain the α'-deformations via a graded version of the Moyal-Weyl product in a class of examples. We conclude with comments on the relation between B- and β-transformations in generalized geometry and the Atiyah algebra on the Drinfel'd double.