Non-Supersymmetric Magic Theories and Ehlers Truncations

We consider the non-supersymmetric magic theories based on the split quaternion and the split complex division algebras. We show that these theories arise as Ehlers $SL(2,mathbb{R})$ and $SL(3,mathbb{R})$ truncations of the maximal supergravity theory, exploiting techniques related to very-extended Kac-Moody algebras. We also generalise the procedure to other $SL(n,mathbb{R})$ truncations, resulting in additional classes of non-supersymmetric theories, as well as to truncations of non-maximal theories. Finally, we discuss duality orbits of extremal black-hole solutions in some of these non-supersymmetric theories.