Geometry of exceptional super Yang-Mills theories

Some time ago, Bars found D = 11 + 3 supersymmetry and Sezgin proposed super Yang-Mills theory (SYM) in D = 11 + 3. Using the "magic star" projection of e(8)(-24), we show that the geometric structure of SYM's in 12 + 4 and 11 + 3 space-time dimensions descends to the affine symmetry of the space AdS(4) circle times S-8. By reducing to transverse transformations along maximal embeddings, the near-horizon geometries of the M2 brane (AdS(4) circle times S-7) and M5 brane (AdS(7) circle times S-4) of M-theory are recovered. Utilizing the recently introduced " exceptional periodicity" (EP) and exploiting the embedding of semisimple rank-3 Jordan algebras into rank-3 T-algebras of special type yields the spaces AdS(4) circle times S-8n and AdS(8n-1) circle times S-5 with reduced subspaces AdS(4) circle times S8n-1 and AdS(8n-1) circle times S-4, respectively. As such, EP describes the nearhorizon geometries of an infinite class of novel exceptional SYM's in (8n + 3) + 3 dimensions that generalize M-theory for n = 1. Remarkably, the n = 3 level hints at M2 and M21 branes as solutions of bosonic M-theory and gives support for Witten's monstrous AdS/CFT construction.