Generalised vielbeins and non-linear realisations

Abstract

We briefly review why the non-linear realisation of the semi-direct product of a group with one of its representations leads to a field theory defined on a generalised space-time equipped with a generalised vielbein. We give formulae, which only involve matrix multiplication, for the generalised vielbein, the Cartan forms and their transformations. We consider the generalised space-time introduced in 2003 in the context of the non-linear realisation of the semi-direct product of E(11) and its first fundamental representation. For this latter theory we give explicit expressions for the generalised vielbein up to and including the levels associated with the dual graviton in four, five and eleven dimensions and for the IIB theory in ten dimensions. We also compute the generalised vielbein, up to the analogous level, for the non-linear realisation of the semi-direct product of very extended SL(2) with its first fundamental representation, which is a theory associated with gravity in four dimensions.

42 pages

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Cited by in corpus (11)

• Beyond E11
• Weaving the Exotic Web
• A brief review of E theory
• Effective Action for Non-Geometric Fluxes from Duality Covariant Actions
• On the exceptional generalised Lie derivative for $d\ge 7$
• All maximal gauged supergravities with uplift
• An E11 invariant gauge fixing
• Gravity, Dual Gravity and A1+++
• Higher dualisations of linearised gravity and the $A_1^{+++}$ algebra
• Unfolding $E_{11}$
• Exotic branes and mixed-symmetry potentials II: Duality rules and exceptional $p$-form gauge fields