The E(11) origin of all maximal supergravities - the hierarchy of field-strengths

Abstract

Starting from $E_{11}$ and the space-time translations we construct an algebra that promotes the global $E_{11}$ symmetries to local ones, and consider all its possible massive deformations. The Jacobi identities imply that such deformations are uniquely determined by a single tensor that belongs to the same representation of the internal symmetry group as the $D-1$ forms specified by $E_{11}$. The non-linear realisation of the deformed algebra gives the field strengths of the theory which are those of any possible gauged maximal supergravity theory in any dimension. All the possible deformed algebras are in one to one correspondence with all the possible massive maximal supergravity theories. The hierarchy of fields inherent in the $E_{11}$ formulation plays an important role in the derivation. The tensor that determines the deformation can be identified with the embedding tensor used previously to parameterise gauged supergravities. Thus we provide a very efficient, simple and unified derivation of the bosonic sector, and in the absence of gravity, of all maximal gauged supergravities from $E_{11}$.

87 pages, 8 figures. Typos corrected, refs added, other minor changes. Version published on JHEP

References in corpus (34)

• Evidence for Heterotic - Type I String Duality
• E_11 and M Theory
• Duality of Type II 7-branes and 8-branes
• E10 and a "small tension expansion" of M Theory
• On Lagrangians and Gaugings of Maximal Supergravities
• Maximal gauged supergravity in three dimensions
• Dualisation of Dualities, II: Twisted self-duality of doubled fields and superdualities
• $E_{11}$, SL(32) and Central Charges
• The maximal D=4 supergravities
• Gauged maximal supergravities and hierarchies of nonabelian vector-tensor systems
• Compact and Noncompact Gauged Maximal Supergravities in Three Dimensions
• The E_{11} origin of all maximal supergravities
• Gauged Supergravities, Tensor Hierarchies, and M-Theory
• The maximal D=5 supergravities
• Very-extended Kac-Moody algebras and their interpretation at low levels
• Magnetic charges in local field theory
• E(11) and the Embedding Tensor
• Generalized E(7(7)) coset dynamics and D=11 supergravity
• Kac-Moody Symmetries of IIB Supergravity
• The maximal D=7 supergravities
• IIB Supergravity Revisited
• E_{11} origin of Brane charges and U-duality multiplets
• (Non-)Abelian Gauged Supergravities in Nine Dimensions
• E(11)-extended spacetime and gauged supergravities
• IIA Ten-forms and the Gauge Algebras of Maximal Supergravity Theories
• The Gaugings of Maximal D=6 Supergravity
• Massive IIA Supergravity as a Non-linear Realisation
• Charge multiplets and masses for E(11)
• On the Yangian Y(e_8) quantum symmetry of maximal supergravity in two dimensions
• On the E10/Massive Type IIA Supergravity Correspondence
• Local E(11)
• E_{11}, ten forms and supergravity
• E10 and Gauged Maximal Supergravity
• Massive Type IIA Supergravity and E10

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• Exploring Double Field Theory
• Duality Invariant Actions and Generalised Geometry
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• Exceptional field theory: $SO(5,5)$
• The O_{D,D} Geometry of String Theory
• The gauge structure of Exceptional Field Theories and the tensor hierarchy
• D-Brane Wess-Zumino Terms and U-Duality
• The tensor hierarchy algebra
• Generalised geometry, eleven dimensions and E11
• Tensor hierarchies, Borcherds algebras and E11
• The general gaugings of maximal d=9 supergravity
• The tensor hierarchy simplified
• E11, generalised space-time and equations of motion in four dimensions
• Off-Shell Hodge Dualities in Linearised Gravity and E11
• Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions
• A brief review of E theory
• Maximal supergravity in three dimensions: supergeometry and differential forms
• Polyvector deformations in eleven-dimensional supergravity
• Generalised Space-time and Gauge Transformations
• On the exceptional generalised Lie derivative for $d\ge 7$
• Forms and algebras in (half-)maximal supergravity theories
• Maximal supergravity in D=10: forms, Borcherds algebras and superspace cohomology
• $L_{\infty }$ algebras and Tensor Hierarchies in Exceptional Field Theory and Gauged Supergravity
• Exceptional Reductions
• Generalised vielbeins and non-linear realisations
• Born sigma model for branes in exceptional geometry
• E11 and exceptional field theory
• Local E(11) and the gauging of the trombone symmetry
• Bound States of String Theory and Beyond
• Higher derivative type II string effective actions, automorphic forms and E11
• E theory in seven dimensions
• Parameters, limits and higher derivative type II string corrections
• Unfolding $E_{11}$
• The very-extended trombone
• Reductions of Exceptional Field Theories