The Intriguing Structure of Non-geometric Frames in String Theory

Abstract

Non-geometric frames in string theory are related to the geometric ones by certain local O(D,D) transformations, the so-called $\beta$-transforms. For each such transformation, we show that there exists both a natural field redefinition of the metric and the Kalb-Ramond two-form as well as an associated Lie algebroid. We furthermore prove that the all-order low-energy effective action of the superstring, written in terms of the redefined fields, can be expressed through differential-geometric objects of the corresponding Lie algebroid. Thus, the latter provides a natural framework for effective superstring actions in non-geometric frames. Relations of this new formalism to double field theory and to the description of non-geometric backgrounds such as T-folds are discussed as well.

46 pages, 1 figure

References in corpus (7)

• Double Field Theory
• Doubled Geometry and T-Folds
• The gauge algebra of double field theory and Courant brackets
• Generalized Geometry and M theory
• T-duality and closed string non-commutative (doubled) geometry
• Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids
• A bi-invariant Einstein-Hilbert action for the non-geometric string

Cited by in corpus (40)

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• Non-geometric backgrounds in string theory
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• Global aspects of double geometry
• The Odd story of ${\alpha }^{\prime }$-corrections
• NS-branes, source corrected Bianchi identities, and more on backgrounds with non-geometric fluxes
• Double Field Theory on Group Manifolds
• The Geometry, Branes and Applications of Exceptional Field Theory
• Non-geometric branes are DFT monopoles
• Consistent Compactification of Double Field Theory on Non-geometric Flux Backgrounds
• Even symplectic supermanifolds and double field theory
• T-duality orbifolds of heterotic Narain compactifications
• Non-commutativity and non-associativity of the doubled string in non-geometric backgrounds
• Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes
• Double Field Theory Inspired Cosmology
• Type IIB flux vacua from G-theory II
• Weaving the Exotic Web
• Type IIB flux vacua from G-theory I
• Sigma models for genuinely non-geometric backgrounds
• Effective Action for Non-Geometric Fluxes from Duality Covariant Actions
• Cosmological Implications from O(D,D)
• Dirac structures on nilmanifolds and coexistence of fluxes
• T-duality, Quotients and Currents for Non-Geometric Closed Strings
• Locally non-geometric fluxes and missing momenta in M-theory
• The monodromy of T-folds and T-fects
• $O(d,d)$ transformations preserve classical integrability
• Poisson-generalized geometry and $R$-flux
• Heterotic Reduction of Courant Algebroid Connections and Einstein-Hilbert Actions
• T-duality, Non-geometry and Lie Algebroids in Heterotic Double Field Theory
• Connecting M-theory and type IIB parameterizations in Exceptional Field Theory
• Towards a world-sheet description of doubled geometry in string theory
• U-dual branes and mixed symmetry tensor fields
• Directly from $H$-flux to the family of three nonlocal $R$-flux theories
• O(d,d)-Duality in String Theory
• Killing sections and sigma models with Lie algebroid targets
• Geometric U-folds in four dimensions
• Open-String Non-Associativity in an R-flux Background
• A gravitational action with stringy $Q$ and $R$ fluxes via deformed differential graded Poisson algebras
• T-duality of a bosonic string in a weakly curved space-time