Large Gauge Transformations in Double Field Theory

Abstract

Finite gauge transformations in double field theory can be defined by the exponential of generalized Lie derivatives. We interpret these transformations as `generalized coordinate transformations' in the doubled space by proposing and testing a formula that writes large transformations in terms of derivatives of the coordinate maps. Successive generalized coordinate transformations give a generalized coordinate transformation that differs from the direct composition of the original two. Instead, it is constructed using the Courant bracket. These transformations form a group when acting on fields but, intriguingly, do not associate when acting on coordinates.

40 pages, v2: discussion of dilaton added, to appear in JHEP

References in corpus (14)

• 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
• T-duality and closed string non-commutative (doubled) geometry
• Generalized E(7(7)) coset dynamics and D=11 supergravity
• Membrane Sigma-Models and Quantization of Non-Geometric Flux Backgrounds
• Ramond-Ramond Cohomology and O(D,D) T-duality
• E11, generalised space-time and IIA string theory
• Rotating string in doubled geometry with generalized isometries
• E11, generalised space-time and IIA string theory; the R-R sector

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