# Exceptional Super Yang-Mills in $D=27+3$ and Worldvolume M-Theory

## TL;DR

This paper explores exceptional super Yang-Mills theories in high-dimensional spacetimes, revealing connections to M-theory, brane dynamics, and algebraic structures like Magic Star algebras and Cayley plane fibers.

## Contribution

It introduces a new super Yang-Mills framework in 27+3 dimensions, linking it to M-theory, branes, and algebraic structures, and proposes a novel realization of spinors via brane cohomologies.

## Key findings

- Super Yang-Mills in 27+3 dimensions with electric 11-brane
- Reduction to 10+1 dimensions models M-theory
- Spinors as cohomologies of extended branes

## Abstract

Bars and Sezgin have proposed a super Yang-Mills theory in $D=s+t=11+3$ space-time dimensions with an electric 3-brane that generalizes the 2-brane of M-theory. More recently, the authors found an infinite family of exceptional super Yang-Mills theories in $D=(8n+3)+3$ via the so-called Magic Star algebras. A particularly interesting case occurs in signature $D=27+3$, where the superalgebra is centrally extended by an electric 11-brane and its 15-brane magnetic dual. The worldvolume symmetry of the 11-brane has signature $D=11+3$ and can reproduce super Yang-Mills theory in $D=11+3$. Upon reduction to $D=26+2$, the 11-brane reduces to a 10-brane with $10+2$ worldvolume signature. A single time projection gives a $10+1$ worldvolume signature and can serve as a model for $D=10+1$ M-theory as a reduction from the $D=26+1$ signature of the bosonic M-theory of Horowitz and Susskind; this is further confirmed by the reduction of chiral $(1,0)$, $D=11+3$ superalgebra to the $\mathcal{N}=1$ superalgebra in $D=10+1$, as found by Rudychev, Sezgin and Sundell some time ago. Extending previous results of Dijkgraaf, Verlinde and Verlinde, we also put forward the realization of spinors as total cohomologies of (the largest spatially extended) branes which centrally extend the $(1,0)$ superalgebra underlying the corresponding exceptional super Yang-Mills theory. Moreover, by making use of an "anomalous" Dynkin embedding, we strengthen Ramond and Sati's argument that M-theory has hidden Cayley plane fibers.