Extended geometries

Abstract

We present a unified and completely general formulation of extended geometry, characterised by a Kac-Moody algebra and a highest weight coordinate module. Generalised diffeomorphisms are constructed, as well as solutions to the section constraint. Generically, additional ("ancillary") gauge transformations are present, and we give a concrete criterion determining when they appear. A universal form of the (pseudo-)action determines the dynamics in all cases without ancillary transformations, and also for a restricted set of cases based on the adjoint representation of a finite-dimensional simple Lie group. Our construction reproduces (the internal sector of) all previously considered cases of double and exceptional field theories.

arXiv comment29 pp. v2: reference added, conclusion section expanded, minor other changes. v3: small changes

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Cited by in corpus (26)

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• A master exceptional field theory
• On supersymmetric E11 exceptional field theory
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• $L_{\infty }$ algebras for extended geometry from Borcherds superalgebras
• Tensor hierarchy algebras and extended geometry II: Gauge structure and dynamics
• $\mathbf{O}(D,D)$ completion of the Friedmann equations
• Tensor hierarchy algebras and extended geometry I: Construction of the algebra
• $L_{\infty }$ algebras and Tensor Hierarchies in Exceptional Field Theory and Gauged Supergravity
• Tensor hierarchy algebra extensions of over-extended Kac--Moody algebras
• Pure spinor superspace action for D=6, N=1 super-Yang-Mills theory
• Infinity-enhancing of Leibniz algebras
• Generators and relations for Lie superalgebras of Cartan type
• Teleparallelism in the algebraic approach to extended geometry
• SL(5) supersymmetry
• Extended geometry of magical supergravities
• Uplifts of maximal supergravities and transitions to non-geometric vacua
• The teleparallel complex
• Towards an extended/higher correspondence -- Generalised geometry, bundle gerbes and global Double Field Theory
• Unfolding $E_{11}$
• $L_{\infty }$ algebras for extended geometry
• Y-algebroids and $E_{7(7)}\times {\mathbb{R}}^{+}$-generalised geometry
• Perturbations in $\mathbf{O}(D,D)$ string cosmology from double field theory
• Supergravity Fluxes and Generalised Geometry
• Pre-NQ Manifolds and Correspondence Spaces: the Nilmanifold Example
• Generators and relations for (generalised) Cartan type superalgebras