K(E10), Supergravity and Fermions

Abstract

We study the fermionic extension of the E10/K(E10) coset model and its relation to eleven-dimensional supergravity. Finite-dimensional spinor representations of the compact subgroup K(E10) of E(10,R) are studied and the supergravity equations are rewritten using the resulting algebraic variables. The canonical bosonic and fermionic constraints are also analysed in this way, and the compatibility of supersymmetry with local K(E10) is investigated. We find that all structures involving A9 levels 0,1 and 2 nicely agree with expectations, and provide many non-trivial consistency checks of the existence of a supersymmetric extension of the E10/K(E10) coset model, as well as a new derivation of the `bosonic dictionary' between supergravity and coset variables. However, there are also definite discrepancies in some terms involving level 3, which suggest the need for an extension of the model to infinite-dimensional faithful representations of the fermionic degrees of freedom.

50 pages

References in corpus (4)

• Hidden symmetries and the fermionic sector of eleven-dimensional supergravity
• Extended E8 Invariance of 11-Dimensional Supergravity
• IIA Ten-forms and the Gauge Algebras of Maximal Supergravity Theories
• IIA and IIB spinors from K(E10)

Cited by in corpus (37)

• The gauge structure of generalised diffeomorphisms
• Spacelike Singularities and Hidden Symmetries of Gravity
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• Beyond E11
• Generalised geometry from the ground up
• IIB Supergravity and the E6(6) covariant vector-tensor hierarchy
• A master exceptional field theory
• On supersymmetric E11 exceptional field theory
• Supersymmetric Domain Walls
• E${}_{8(8)}$ Exceptional Field Theory: Geometry, Fermions and Supersymmetry
• Quantum Supersymmetric Bianchi IX Cosmology
• Constraints and the E10 Coset Model
• SO(9) supergravity in two dimensions
• On the E10/Massive Type IIA Supergravity Correspondence
• K(E9) from K(E10)
• Planck Mass Charged Gravitino Dark Matter
• Fermionic Kac-Moody Billiards and Supergravity
• Dual Gravity and Matter
• Standard Model Fermions and Infinite-Dimensional R-Symmetries
• E10 and Gauged Maximal Supergravity
• On higher spin realizations of K(E10)
• Quantum Einstein-Dirac Bianchi Universes
• Representations of involutory subalgebras of affine Kac-Moody algebras
• An M-theory solution from null roots in E11
• Pure type I supergravity and DE(10)
• Symmetries of M-theory and free Lie superalgebras
• Canonical structure of the E10 model and supersymmetry
• The E10 Wheeler-DeWitt operator at low levels
• Quantum Supersymmetric Cosmological Billiards and their Hidden Kac-Moody Structure
• Supermassive gravitinos and giant primordial black holes
• On the underlying E11 symmetry of the D=11 Free Differential Algebra
• Generalised holonomies and K(E${}_9$)
• Unfolding $E_{11}$
• Asymptotic safety and quantum gravity amplitudes
• The M-algebra completes the hierarchy of Super-Exceptional Tangent Spaces
• Massive Type IIA Supergravity and E10
• Hidden Kac-Moody Structures in the Fermionic Sector of Five-Dimensional Supergravity