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We consider the dimensional reduction to D = 3 of four maximal-rank super-gravities which preserve minimal supersymmetry in D = 11, 7, 5 and 4. Such “curious” theories were investigated some time ago, and the four-dimensional one corresponds to an \( \mathcal{N}=1 \) supergravity with 7 chiral multiplets spanning the seven-disk manifold. Recently, this latter theory provided...

We give an octonionic formulation of the \( \mathcal{N}=1 \) supersymmetry algebra in D = 11, including all brane charges. We write this interms of a novel outer product, which takes a pair of elements of the division algebra \( \mathbb{A} \) and returns a real linear operator on \( \mathbb{A} \) . More generally, with this product comes the power to rewrite any linear operation...

We give a unified division algebraic description of (D = 3, \( \mathcal{N} \) = 1, 2, 4, 8), (D = 4, \( \mathcal{N} \) = 1, 2, 4), (D = 6, \( \mathcal{N} \) = 1, 2) and (D = 10, \( \mathcal{N} \) = 1) super Yang-Mills theories. A given (D = n + 2, \( \mathcal{N} \)) theory is completely specified by selecting a pair (\( {\mathbb{A}}_n \), \( {{\mathbb{A}}_n}_{\mathcal{N}} \)) of...

By formulating \( \mathcal{N} \) = 1, 2, 4, 8, D = 3, Yang-Mills with a single Lagrangian and single set of transformation rules, but with fields valued respectively in \( \mathbb{R},\mathbb{C},\mathbb{H},\mathbb{O} \) , it was recently shown that tensoring left and right multiplets yields a Freudenthal-Rosenfeld-Tits magic square of D = 3 supergravities. This was subsequently...