A note on Faddeev--Popov action for doubled-yet-gauged particle and graded Poisson geometry

Abstract

The section condition of Double Field Theory has been argued to mean that doubled coordinates are gauged: a gauge orbit represents a single physical point. In this note, we consider a doubled and at the same time gauged particle action, and show that its BRST formulation including Faddeev--Popov ghosts matches with the graded Poisson geometry that has been recently used to describe the symmetries of Double Field Theory. Besides, by requiring target spacetime diffeomorphisms at the quantum level, we derive quantum corrections to the classical action involving dilaton, which might be comparable with the Fradkin--Tseytlin term on string worldsheet.

arXiv comment22 pages = 1 + 14 + references; v2) minor changes, final version

References in corpus (58)

• Double Field Theory
• Generalized metric formulation of double field theory
• A Geometry for Non-Geometric String Backgrounds
• Background independent action for double field theory
• New Supersymmetric String Compactifications
• Doubled Geometry and T-Folds
• The gauge algebra of double field theory and Courant brackets
• Higher derived brackets and homotopy algebras
• Supergravity as Generalised Geometry I: Type II Theories
• Differential geometry with a projection: Application to double field theory
• Derived brackets
• Double Field Theory of Type II Strings
• Stringy differential geometry, beyond Riemann
• Unification of Type II Strings and T-duality
• Double Field Theory Formulation of Heterotic Strings
• On the Riemann Tensor in Double Field Theory
• Non-geometric backgrounds, doubled geometry and generalised T-duality
• Large Gauge Transformations in Double Field Theory
• 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
• Comments on double field theory and diffeomorphisms
• Incorporation of fermions into double field theory
• Ramond-Ramond Cohomology and O(D,D) T-duality
• Global aspects of double geometry
• On the geometry of double field theory
• Double field formulation of Yang-Mills theory
• Finite Gauge Transformations and Geometry in Double Field Theory
• Towards a double field theory on para-Hermitian manifolds
• Double Field Theory and Membrane Sigma-Models
• A Unique Connection for Born Geometry
• The geometry behind double geometry
• A worldsheet supersymmetric Newton-Cartan string
• Einstein Double Field Equations
• Even symplectic supermanifolds and double field theory
• Generalised Kinematics for Double Field Theory
• $\mathbf{O}(D,D)$ Covariant Noether Currents and Global Charges in Double Field Theory
• Algebroid Structures on Para-Hermitian Manifolds
• 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
• Weyl invariance of string theories in generalized supergravity backgrounds
• Green-Schwarz superstring on doubled-yet-gauged spacetime
• The rotation curve of a point particle in stringy gravity
• Para-Hermitian Geometry, Dualities and Generalized Flux Backgrounds
• The Exceptional Sigma Model
• Generalised Geometry and type II Supergravity
• Para-Hermitian Geometries for Poisson-Lie Symmetric $\sigma$-models
• Standard Model as a Double Field Theory
• Doubled Aspects of Vaisman Algebroid and Gauge Symmetry in Double Field Theory
• Doubling, T-Duality and Generalized Geometry: a Simple Model
• Extended Riemannian Geometry II: Local Heterotic Double Field Theory
• Type II strings are Exceptional
• Towards a world-sheet description of doubled geometry in string theory
• Stringy Gravity: Solving the Dark Problems at `short' distance
• The different faces of branes in Double Field Theory
• Extended Riemannian Geometry III: Global Double Field Theory with Nilmanifolds
• T-Dualities and Doubled Geometry of the Principal Chiral Model
• Higher Spin Double Field Theory : A Proposal

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• The Geometry, Branes and Applications of Exceptional Field Theory
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