The Gauge algebra of double field theory and Courant brackets

By C. Hull, B. Zwiebach. 2009

435 citations recorded by the source corpus.

We investigate the symmetry algebra of the recently proposed field theory on a doubled torus that describes closed string modes on a torus with both momentum and winding. The gauge parameters are constrained fields on the doubled space and transform as vectors under T-duality. The gauge algebra defines a T-duality covariant bracket. For the case in which the parameters and fields are T-dual to ones that have momentum but no winding, we find the gauge transformations to all orders and show that the gauge algebra reduces to one obtained by Siegel. We show that the bracket for such restricted parameters is the Courant bracket. We explain how these algebras are realised as symmetries despite the failure of the Jacobi identity.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ad0a123cca6c390b2c45a1bc2600d9fdd392fae9

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Citations in the corpus

Background independent action for double field theory (2010, methodology): “With this strong constraint we were able [3] to find a consistent set of gauge transformations to all orders and show that their gauge algebra is governed by the Courant bracket of generalised geometry [7, 8, 9, 10, 11].”
Double field theory formulation of heterotic strings (2011, background): “19) Here, JC is the Jacobiator of the C-bracket, which has been proved in [2] to be a gradient.”
Double Field Theory and N=4 Gauged Supergravity (2011, background): “Moreover, this theory has a local gauge symmetry [3] generated by a generalized Lie derivative which is an extension for doubled coordinates of the Dorfmann bracket appearing in Generalized Complex Geometry [4].”
Duality invariant actions and generalised geometry (2011, background): “The extra dimensions are M-theoretic generalisations of the winding coordinates found in doubled field theory [40, 41, 42, 43].”
Duality Symmetric String and M-Theory (2013, methodology): “Of course, the full closed string field theory is a huge challenge and the work of Hull and Zwiebach focuses on a tractable truncation to the massless sector and in particular to the N = N̄ = 1 sector.”
Generalized metric formulation of double field theory (2010, background): “Generalized vectors that depend just on x and not on x̃ decompose into a vector and a 1-form on the usual D-dimensional space with coordinates x, and in that case it was shown in [3] that the C bracket becomes precisely the Courant bracket.”
Duality orbits of non‐geometric fluxes (2012, background): “DFT is a recent proposal that promotes T-duality to a symmetry in field theory [6, 11], and is currently defined in terms of a background independent action [12].”
The local symmetries of M-theory and their formulation in generalised geometry (2011, positive): “In string theory this has led to the doubled geometry approach [7–10] where the target space of the string is doubled and the metric on this space is given by the metric of generalised geometry of the sort developed by Hitchin and Gualtieri [11–13].”
A ten-dimensional action for non-geometric fluxes (2011, background): “Double field theory (DFT) has been introduced in [73, 74, 75, 20] and developed in a series of subsequent papers.”
Membrane sigma-models and quantization of non-geometric flux backgrounds (2012, background): “The relevance of Courant algebroids in nongeometric flux compactifications and to gauge symmetries in double field theory has also been noted in [34, 46, 9].”
Extended geometry and gauged maximal supergravity (2013, background): “The program to rewrite the theory in a covariant language under O(d, d), the group that includes T-duality, goes under the name of Generalized Geometry [1, 2], or Double Field Theory (DFT) [3–6] (the latter based on previous constructions on”