Supergravity solution-generating techniques and canonical transformations of $\sigma$-models from $O(D,D)$

TL;DR

This paper explores solution-generating techniques in supergravity and canonical transformations in 2D sigma-models derived from Double Field Theory, including known and novel dualities and deformations, without requiring the supergravity equations of motion.

Contribution

It introduces a unified framework for generating supergravity solutions and sigma-model transformations via generalized fluxes and twists in Double Field Theory, encompassing known and new dualities.

Findings

Classified twists leading to constant generalized fluxes.

Identified transformations preserving fluxes, including known dualities.

Provided new generalizations of T-duality and Yang-Baxter deformations.

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 $H_{ijk}, F_{ij}{}^k, Q_i{}^{jk}$ and $R^{ijk}$, 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 $\sigma$-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 $\sigma$-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.