# Geometry of exceptional super Yang-Mills theories

Rios, Michael (Dyonica ICMQG, Los Angeles, 90032 California, USA) ; Marrani, Alessio (Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi, Via Panisperna 89A, I-00184 Roma, Italy) ; Chester, David (Department of Physics and Astronomy, UCLA, Los Angeles, 90024 California, USA)

13 February 2019

Abstract: 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 ${e}_{8\left(-24\right)}$, 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 ${\mathrm{AdS}}_{4}\otimes {S}^{8}$. By reducing to transverse transformations along maximal embeddings, the near-horizon geometries of the M2 brane (${\mathrm{AdS}}_{4}\otimes {S}^{7}$) and M5 brane (${\mathrm{AdS}}_{7}\otimes {S}^{4}$) 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 ${\mathrm{AdS}}_{4}\otimes {S}^{8n}$ and ${\mathrm{AdS}}_{8n-1}\otimes {S}^{5}$ with reduced subspaces ${\mathrm{AdS}}_{4}\otimes {S}^{8n-1}$ and ${\mathrm{AdS}}_{8n-1}\otimes {S}^{4}$, respectively. As such, EP describes the near-horizon geometries of an infinite class of novel exceptional SYM’s in $\left(8n+3\right)+3$ 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.

Published in: Physical Review D 99 (2019)