Comments on double field theory and diffeomorphisms

Abstract

As the theory is subject to a section condition, coordinates in double field theory do not represent physical points in an injective manner. We argue that a physical point should be rather one-to-one identified with a `gauge orbit' in the coordinate space. The diffeomorphism symmetry then implies an invariance under arbitrary reparametrizations of the gauge orbits. Within this generalized sense of diffeomorphism, we show that a recently proposed tensorial transformation rule for finite coordinate transformations is actually (i) consistent with the standard exponential map, and further (ii) compatible with the full covariance of the `semi-covariant' derivatives and curvatures after projectors are properly imposed.

1+34 pages; A minute change of the title from "diffeomorphism" to "diffeomorphisms". To appear in JHEP

References in corpus (15)

• Double Field Theory
• The gauge algebra of double field theory and Courant brackets
• Generalized Geometry and M theory
• Differential geometry with a projection: Application to double field theory
• Gauged Double Field Theory
• Duality orbits of non-geometric fluxes
• Double Field Theory Formulation of Heterotic Strings
• Extended geometry and gauged maximal supergravity
• Lectures on Generalized Complex Geometry for Physicists
• Ramond-Ramond Cohomology and O(D,D) T-duality
• Double field formulation of Yang-Mills theory
• Gauged supergravities in 5 and 6 dimensions from generalised Scherk-Schwarz reductions
• U-geometry : SL(5)
• E8 duality and dual gravity
• Superconformal Yang-Mills quantum mechanics and Calogero model with OSp(N|2,R) symmetry

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