M-theory (and F-theory) from D=27+3

As the M-theory and Mathematics conference takes place in Abu-Dhabi, it’s great time to reflect on talks from last year.  In D=26+1 the M-theory superalgebra permits a 10-brane, with D=10+1 worldvolume signature.  This gives a worldvolume interpretation of 11D M-theory in 27-dimensions.  However, to include F-theory as well one is required to have at least a D=11+3 worldvolume theory, whose superalgebra takes the form specified by Sezgin et al. in hep-th/9711127.  Such a worldvolume exists in D=27+3, where an 11-brane sweeps out an (11,3) signature worldvolume.  Here string dualities are related to the various geometric reductions of this 11-brane worldvolume theory.