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IIA and IIB spinors from K(E10)

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Kleinschmidt,  Axel
Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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Nicolai,  Hermann
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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264908.pdf
(Publisher version), 157KB

0603205.pdf
(Preprint), 197KB

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Citation

Kleinschmidt, A., & Nicolai, H. (2006). IIA and IIB spinors from K(E10). Physics Letters B, 637(1-2), 107-112. doi:10.1016/j.physletb.2006.04.007.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-4BDB-7
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.