Abstract
Within the framework of the flux formulation of Double Field Theory (DFT) we employ a generalised Scherk-Schwarz ansatz and discuss the classification of the twists that in the presence of the strong constraint give rise to constant generalised fluxes interpreted as gaugings. We analyse the various possibilities of turning on the fluxes Hijk, Fijk, Qijk and Rijk, and the solutions for the twists allowed in each case. While we do not impose the DFT (or equivalently supergravity) equations of motion, our results provide solution-generating techniques in supergravity when applied to a background that does solve the DFT equations. At the same time, our results give rise also to canonical transformations of 2-dimensional σ-models, a fact which is interesting especially because these are integrability-preserving transformations on the worldsheet. Both the solution-generating techniques of supergravity and the canonical transformations of 2-dimensional σ-models arise as maps that leave the generalised fluxes of DFT and their flat derivatives invariant. These maps include the known abelian/non-abelian/Poisson-Lie T-duality transformations, Yang-Baxter deformations, as well as novel generalisations of them.
Highlights
An important concept in physics is that of symmetry
In appendix A we collect our conventions on notation, in appendix B we give a brief recap on some aspects of Double Field Theory (DFT) and gauged DFT that are relevant for our discussion, in appendix C we discuss how to obtain the parametrisation of the twist that we use, in appendix D we give more details on the formulations to include the RR fields of type II, in appendix E we review the DFT equations of motion in the flux
We have discussed an ansatz for the generalised vielbein of DFT by demanding that it takes a “twisted” form, as in generalised Scherk-Schwarz reductions of D-dimensional backgrounds on d-dimensional spaces, and that the twist U gives rise to constant generalised
Summary
An important concept in physics is that of symmetry. Symmetries are powerful tools to constrain the form of solutions of physical theories, and they may be used as a guiding principle to construct new physical models. Our strategy is to rewrite the D-dimensional fields in terms of the doubled fields of DFT, and demand that Gmn, Bmn, φ and Gmn, Bmn, φ give rise to the same generalised fluxes and flat derivatives F = F , ∂F = ∂F This is a sufficient condition to have again a (super)gravity solution, and it is the mechanism that applies for the generalised T-duality transformations.. When two different σ-models admit a rewriting of the phase-space variables in terms of ΨA and ΨA respectively, and when they give rise to the same generalised fluxes FABC when computing the Poisson brackets, the two σ-models are related by a canonical transformation — possibly up to zero modes This last remark is a consequence of the fact that only the spatial derivative of the coordinates xm appear in ΨM , and with the above argument one is not able to claim that the zero-mode contribution to the Poisson brackets remains invariant under the map. Formulation, and in appendix F we report on other attempts we made to treat orbits with non-vanishing H-flux
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
