Alessio Marrani, Universidad de Murcia, Spain

**Title**: Exceptional super Yang-Mills in 27 + 3 and worldvolume M-theory

**Abstract**: Some time ago, Bars and Sezgin 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, Rios, Chester and the speaker found an infinite family of "exceptional" super Yang-Mills theories in D=s+t=(8n+3)+3. A particularly interesting case occurs for n=3, namely in signature D=27+3, in which 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 it 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 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, I will 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, I will present further evidence about Ramond's and Sati's argument that M-theory has hidden Cayley plane fibers.

Reference : https://arxiv.org/abs/1906.10709