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We consider all theories with eight supersymmetries whose reduction to threedimensions gives rise to scalars that parametrise symmetric manifolds. Weconjecture that these theories are non-linear realisations of very-extendedKac-Moody algebras for suitable choices of real forms. We show for the mostinteresting cases that the bosonic sector of the supersymmetric theory isprecisely reproduced by the corresponding non-linear realisation.

Real forms of very extended Kac-Moody algebras and theories with eight supersymmetries