David Chester, Alessio Marrani, Michael Rios (2019)
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 e8(−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 AdS4⊗S8. By reducing to transverse transformations along maximal embeddings, the near-horizon geometries of the M2 brane (AdS4⊗S7) and M5 brane (AdS7⊗S4) 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 AdS4⊗S8n and AdS8n−1⊗S5 with reduced subspaces AdS4⊗S8n−1 and AdS8n−1⊗S4, respectively. As such, EP describes the near-horizon 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.