Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-03-27
Phys.Lett.B637:107-112,2006
Physics
High Energy Physics
High Energy Physics - Theory
16 pages, v2: added paragraph on spinors for K(E9) and K(E11)
Scientific paper
10.1016/j.physletb.2006.04.007
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.
Kleinschmidt Axel
Nicolai Hermann
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