Bianchi Identities for Non-Geometric Fluxes - From Quasi-Poisson Structures to Courant Algebroids

Abstract

Starting from a (non-associative) quasi-Poisson structure, the derivation of a Roytenberg-type algebra is presented. From the Jacobi identities of the latter, the most general form of Bianchi identities for fluxes (H,f,Q,R) is then derived. It is also explained how this approach is related to the mathematical theory of quasi-Lie and Courant algebroids.

17 pages; v2: references added, typos corrected

References in corpus (6)

• Double Field Theory
• Doubled Geometry and T-Folds
• The gauge algebra of double field theory and Courant brackets
• T-duality and closed string non-commutative (doubled) geometry
• Toroidal Orientifolds in IIA with General NS-NS Fluxes
• Non-geometric Backgrounds and the First Order String Sigma Model

Cited by in corpus (36)

• Exploring Double Field Theory
• M-theory and Type IIB from a Duality Manifest Action
• Non-geometric backgrounds in string theory
• β-supergravity: a ten-dimensional theory with non-geometric fluxes, and its geometric framework
• Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids
• NS-branes, source corrected Bianchi identities, and more on backgrounds with non-geometric fluxes
• Duality Symmetric String and M-Theory
• Double Field Theory and Membrane Sigma-Models
• A bi-invariant Einstein-Hilbert action for the non-geometric string
• Even symplectic supermanifolds and double field theory
• Matrix theory origins of non-geometric fluxes
• Algebroid Structures on Para-Hermitian Manifolds
• Unified picture of non-geometric fluxes and T-duality in double field theory via graded symplectic manifolds
• Non-commutativity and non-associativity of the doubled string in non-geometric backgrounds
• Dimensional Oxidation of Non-geometric Fluxes in Type II Orientifolds
• Revisiting the two formulations of Bianchi identities and their implications on moduli stabilization
• On current algebras, generalised fluxes and non-geometry
• Dirac structures on nilmanifolds and coexistence of fluxes
• Double field theory for the A/B-models and topological S-duality in generalized geometry
• Fluxes in Exceptional Field Theory and Threebrane Sigma-Models
• Poisson-generalized geometry and $R$-flux
• D-brane on Poisson manifold and Generalized Geometry
• AKSZ constructions for topological membranes on $G_2$-manifolds
• More on Doubled Aspects of Algebroids in Double Field Theory
• On Missing Bianchi Identities in Cohomology Formulation
• O(d,d)-Duality in String Theory
• Courant bracket twisted both by a 2-form $B$ and by a bi-vector $\theta$
• Twisted C-brackets
• Lie algebroids, non-associative structures and non-geometric fluxes
• BRST symmetry of doubled membrane sigma-models
• Fluxes of Courant bracket twisted at the same time by $B$ and $\theta$
• The geometric constraints on Filippov algebroids
• A gravitational action with stringy $Q$ and $R$ fluxes via deformed differential graded Poisson algebras
• Supergravity solution-generating techniques and canonical transformations of $\sigma$-models from $O(D,D)$
• Higher dimensional Lie algebroid sigma model with WZ term
• $L_{\infty }$-algebras and membrane sigma models