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

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.

arXiv comment58 pages, 1 figure, 6 appendices; v2: published version, references and minor clarifications added, notational fixes

References in corpus (50)

• Double Field Theory
• Generalized metric formulation of double field theory
• Superspace Duality in Low-Energy Superstrings
• On integrability of the Yang-Baxter $\si$-model
• An integrable deformation of the AdS_5 x S^5 superstring action
• Duality Symmetries from Non--Abelian Isometries in String Theories
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• New Formulations of D=10 Supersymmetry and D8-O8 Domain Walls
• Integrable interpolations: From exact CFTs to non-Abelian T-duals
• Courant algebroids, derived brackets and even symplectic supermanifolds
• Poisson-Lie T-duality and Loop Groups of Drinfeld Doubles
• Double Field Theory and N=4 Gauged Supergravity
• Exploring Double Field Theory
• Scale invariance of the eta-deformed AdS5 x S5 superstring, T-duality and modified type II equations
• On non-abelian T-dual geometries with Ramond fluxes
• Double Field Theory of Type II Strings
• On integrable deformations of superstring sigma models related to AdS_n x S^n supercosets
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• Duality orbits of non-geometric fluxes
• An Integrable Deformation of the AdS5 x S5 Superstring
• Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
• Generalised integrable $\lambda$- and $\eta$-deformations and their relation
• $\eta$ and $\lambda$ deformations as $\mathcal{E}$-models
• Abelian Yang-Baxter Deformations and TsT transformations
• Non-abelian T-duality, Ramond Fields and Coset Geometries
• Large Gauge Transformations in Double Field Theory
• Spacetimes for λ-deformations
• A Problem with Non-Abelian Duality
• Integrable deformations of T-dual $\sigma$ models
• Yang-Baxter $\sigma$-models, conformal twists, and noncommutative Yang-Mills theory
• Poisson-Lie T-Duality in Double Field Theory
• Doubled aspects of generalised dualities and integrable deformations
• The all-loop non-Abelian Thirring model and its RG flow
• Canonical equivalence of non-isometric sigma models and Poisson-Lie T-duality
• Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings
• Generalized Metric Formulation of Double Field Theory on Group Manifolds
• Bianchi Identities for Non-Geometric Fluxes - From Quasi-Poisson Structures to Courant Algebroids
• $T$-folds from Yang-Baxter deformations
• Non-geometric Backgrounds and the First Order String Sigma Model
• Quantum correction to generalized T-dualities
• O(D,D) and the string ${\alpha }^{\prime }$ expansion: An obstruction
• Integrable deformations of the $G_{k_1}\times G_{k_2}/G_{k_1+k_2}$ coset CFTs
• Yang-Baxter deformations of the Principal Chiral Model plus Wess-Zumino term
• The type II superstring to order theta^4
• Para-Hermitian Geometries for Poisson-Lie Symmetric $\sigma$-models
• BTZ black hole from Poisson-Lie T-dualizable sigma models with spectators
• Exact conformal field theories from mutually T-dualizable $\sigma$-models
• T-duality and T-folds for point particles
• Integrable $\lambda$-deformations of the Euclidean black string
• Poisson-Lie T-plurality for WZW backgrounds

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