Remarks on the non-Riemannian sector in Double Field Theory

Abstract

Taking $\mathbf{O}(D,D)$ covariant field variables as its truly fundamental constituents, Double Field Theory can accommodate not only conventional supergravity but also non-Riemannian gravities that may be classified by two non-negative integers, $(n,\bar{n})$. Such non-Riemannian backgrounds render a propagating string chiral and anti-chiral over $n$ and $\bar{n}$ dimensions respectively. Examples include, but are not limited to, Newton--Cartan, Carroll, or Gomis--Ooguri. Here we analyze the variational principle with care for a generic $(n,\bar{n})$ non-Riemannian sector. We recognize a nontrivial subtlety for $n\bar{n}\ne 0$ that infinitesimal variations generically include those which change $(n,\bar{n})$. This seems to suggest that the various non-Riemannian gravities should better be identified as different solution sectors of Double Field Theory rather than viewed as independent theories. Separate verification of our results as string worldsheet beta-functions may enlarge the scope of the string landscape far beyond Riemann.

arXiv comment44 pages = 30 pages + Appendix + References; v2) Refs added, minor changes, final version

References in corpus (83)

• Double Field Theory
• Generalized metric formulation of double field theory
• Superspace Duality in Low-Energy Superstrings
• A Geometry for Non-Geometric String Backgrounds
• Two-Vierbein Formalism for String-Inspired Axionic Gravity
• Background independent action for double field theory
• U-duality and M-Theory
• Doubled Geometry and T-Folds
• Double Field Theory: A Pedagogical Review
• The gauge algebra of double field theory and Courant brackets
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• The Spacetime of Double Field Theory: Review, Remarks, and Outlook
• Non-Relativistic Closed String Theory
• Torsional Newton-Cartan Geometry and Lifshitz Holography
• Differential geometry with a projection: Application to double field theory
• Double Field Theory of Type II Strings
• Stringy differential geometry, beyond Riemann
• A ten-dimensional action for non-geometric fluxes
• Action Principle for Newtonian Gravity
• Duality orbits of non-geometric fluxes
• Unification of Type II Strings and T-duality
• `Stringy' Newton-Cartan Gravity
• Double Field Theory Formulation of Heterotic Strings
• On the Riemann Tensor in Double Field Theory
• Strings with Non-Relativistic Conformal Symmetry and Limits of the AdS/CFT Correspondence
• Supersymmetric Double Field Theory: Stringy Reformulation of Supergravity
• Introducing Cadabra: a symbolic computer algebra system for field theory problems
• Nonrelativistic String Theory and T-Duality
• Covariant action for a string in doubled yet gauged spacetime
• Stringy Unification of Type IIA and IIB Supergravities under N=2 D=10 Supersymmetric Double Field Theory
• Non-Geometric Fluxes in Supergravity and Double Field Theory
• Background Field Equations for the Duality Symmetric String
• M-theory and Type IIB from a Duality Manifest Action
• Three-Dimensional Extended Bargmann Supergravity
• Geometry and fluxes of SL(5) exceptional field theory
• Comments on double field theory and diffeomorphisms
• Galilean Isometries
• Non-geometric backgrounds in string theory
• β-supergravity: a ten-dimensional theory with non-geometric fluxes, and its geometric framework
• Incorporation of fermions into double field theory
• Gauged Supergravities from Twisted Doubled Tori and Non-Geometric String Backgrounds
• Ramond-Ramond Cohomology and O(D,D) T-duality
• Heterotic Effective Action and Duality Symmetries Revisited
• Non-Relativistic Chern-Simons Theories and Three-Dimensional Horava-Lifshitz Gravity
• Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids
• Supersymmetry for Gauged Double Field Theory and Generalised Scherk-Schwarz Reductions
• Connections and dynamical trajectories in generalised Newton-Cartan gravity II. An ambient perspective
• Connections and dynamical trajectories in generalised Newton-Cartan gravity I. An intrinsic view
• Double field formulation of Yang-Mills theory
• Finite Gauge Transformations and Geometry in Double Field Theory
• Flux Compactifications of String Theory on Twisted Tori
• Strings and Branes are Waves
• Non-geometric Fluxes, Asymmetric Strings and Nonassociative Geometry
• Double Field Theory and Membrane Sigma-Models
• A Double Sigma Model for Double Field Theory
• Non-geometric branes are DFT monopoles
• A worldsheet supersymmetric Newton-Cartan string
• Einstein Double Field Equations
• Consistent Compactification of Double Field Theory on Non-geometric Flux Backgrounds
• An Action for Extended String Newton-Cartan Gravity
• Type II DFT solutions from Poisson-Lie T-duality/plurality
• $\mathbf{O}(D,D)$ Covariant Noether Currents and Global Charges in Double Field Theory
• Amplitudes for left-handed strings
• T-duality and non-geometric solutions from double geometry
• Non-Riemannian geometry of M-theory
• Unified picture of non-geometric fluxes and T-duality in double field theory via graded symplectic manifolds
• The rotation curve of a point particle in stringy gravity
• Green-Schwarz superstring on doubled-yet-gauged spacetime
• E11, generalised space-time and IIA string theory; the R-R sector
• Para-Hermitian Geometry, Dualities and Generalized Flux Backgrounds
• The Exceptional Sigma Model
• Timelike U-dualities in Generalised Geometry
• Kaluza-Klein reduction on a maximally non-Riemannian space is moduli-free
• Supersymmetric gauged Double Field Theory: Systematic derivation by virtue of \textit{Twist}
• Effective Action for Non-Geometric Fluxes from Duality Covariant Actions
• Standard Model as a Double Field Theory
• p-brane Newton--Cartan Geometry
• Windings of twisted strings
• U-gravity : $\mathbf{SL}(N)$
• Type II strings are Exceptional
• Stringy Gravity: Solving the Dark Problems at `short' distance
• Extended Riemannian Geometry III: Global Double Field Theory with Nilmanifolds
• Higher Spin Double Field Theory : A Proposal

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