A bi-invariant Einstein-Hilbert action for the non-geometric string

Abstract

Inspired by recent studies on string theory with non-geometric fluxes, we develop a differential geometry calculus combining usual diffeomorphisms with what we call beta-diffeomorphisms. This allows us to construct a manifestly bi-invariant Einstein-Hilbert type action for the graviton, the dilaton and a dynamical (quasi-)symplectic structure. The equations of motion of this symplectic gravity theory, further generalizations and the relation to the usual form of the string effective action are discussed. The Seiberg-Witten limit, known for open strings to relate commutative with non-commutative theories, makes an interesting appearance.

4 pages; v2: references added, typos corrected; v3: published version

References in corpus (20)

• String Theory and Noncommutative Geometry
• Double Field Theory
• Superspace Duality in Low-Energy Superstrings
• Background independent action for double field theory
• Nongeometric Flux Compactifications
• Supergravity as Generalised Geometry I: Type II Theories
• The gauge structure of generalised diffeomorphisms
• T-duality, Generalized Geometry and Non-Geometric Backgrounds
• A ten-dimensional action for non-geometric fluxes
• T-duality and closed string non-commutative (doubled) geometry
• A geometric action for non-geometric fluxes
• Nonassociative Gravity in String Theory?
• Nonassociative tori and applications to T-duality
• Non-Geometric Fluxes in Supergravity and Double Field Theory
• The effective action of Double Field Theory
• Membrane Sigma-Models and Quantization of Non-Geometric Flux Backgrounds
• Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids
• Non-geometric Fluxes, Asymmetric Strings and Nonassociative Geometry
• Bianchi Identities for Non-Geometric Fluxes - From Quasi-Poisson Structures to Courant Algebroids
• Non-geometric String Backgrounds and Worldsheet Algebras

Cited by in corpus (34)

• Double Field Theory: A Pedagogical Review
• The Spacetime of Double Field Theory: Review, Remarks, and Outlook
• 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
• Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT's
• (Non-)commutative closed string on T-dual toroidal backgrounds
• Non-geometric branes are DFT monopoles
• Consistent Compactification of Double Field Theory on Non-geometric Flux Backgrounds
• The Intriguing Structure of Non-geometric Frames in String Theory
• Non-commutative/non-associative IIA (IIB) Q- and R-branes and their intersections
• Dimensional Oxidation of Non-geometric Fluxes in Type II Orientifolds
• Non-commutativity and non-associativity of the doubled string in non-geometric backgrounds
• Weaving the Exotic Web
• T-duality revisited
• Effective Action for Non-Geometric Fluxes from Duality Covariant Actions
• Cosmological Implications from O(D,D)
• On T-duality transformations for the three-sphere
• Locally non-geometric fluxes and missing momenta in M-theory
• The monodromy of T-folds and T-fects
• Connecting M-theory and type IIB parameterizations in Exceptional Field Theory
• Towards a world-sheet description of doubled geometry in string theory
• Gauge Transformation of Double Field Theory for Open String
• Dimensional Reduction of the Generalized DBI
• On Inflation and de Sitter in Non-Geometric String Backgrounds
• Directly from $H$-flux to the family of three nonlocal $R$-flux theories
• Lie algebroids, non-associative structures and non-geometric fluxes
• A class of non-geometric M-theory compactification backgrounds
• Open-String Non-Associativity in an R-flux Background
• T-duality of a bosonic string in a weakly curved space-time
• A gravitational action with stringy $Q$ and $R$ fluxes via deformed differential graded Poisson algebras