IIA and IIB spinors from K(E10)

Abstract

We analyze the decomposition of recently constructed unfaithful spinor representations of K(E10) under its SO(9) x SO(9), and SO(9) x SO(2) subgroups, respectively, where K(E10) is the `maximal compact' subgroup of the hyperbolic Kac--Moody group E(10). We show that under these decompositions, respectively, one and the same K(E10) spinor gives rise to both the fermionic fields of IIA supergravity, and to the (chiral) fermionic fields of IIB supergravity. This result is thus the fermionic analogue of the decomposition of E(10) under its SO(9,9) and SL(9) x SL(2) subgroups, respectively, which yield the correct bosonic multiplets of (massive) IIA and IIB supergravity. The essentially unique Lagrangian for the supersymmetric E(10)/K(E10) sigma-model therefore can also capture the dynamics of IIA and IIB including bosons and fermions in the known truncations.

16 pages, v2: added paragraph on spinors for K(E9) and K(E11)

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Cited by in corpus (16)

• K(E10), Supergravity and Fermions
• A master exceptional field theory
• On supersymmetric E11 exceptional field theory
• Constraints and the E10 Coset Model
• On the E10/Massive Type IIA Supergravity Correspondence
• K(E9) from K(E10)
• On higher spin realizations of K(E10)
• Representations of involutory subalgebras of affine Kac-Moody algebras
• Arithmetic and Hyperbolic Structures in String Theory
• Pure type I supergravity and DE(10)
• Unfolding $E_{11}$
• Generalised holonomies and K(E${}_9$)
• Unifying R-symmetry in M-theory
• Aspects of electric-magnetic dualities in maximal supergravity
• Massive Type IIA Supergravity and E10
• The M-algebra completes the hierarchy of Super-Exceptional Tangent Spaces