Exceptional field theories, superparticles in an enlarged 11D superspace and higher spin theories

In this paper we show how the hypothesis on the relation of all the known En(n) EFTs, including n=8, with supersymmetry leads to the conjecture on existence of 11D exceptional field theory living in 11D tensorial central charge superspace Σ(528|32) and underlying all the En(n) EFTs with n=2,...,8, and probably the double field theory (DFT). We conjecture the possible form of the section conditions of such an 11D EFT and show that quite generic solutions of these can be generated by superparticle models the ground states of which preserve from one half to all but one supersymmetry. The properties of these superparticle models are briefly discussed. We argue that, upon quantization, their quantum states should describe free massless non-conformal higher spin fields in D=11. We also discuss some relevant representations of the M-theory superalgebra which, in the present context, describes supersymmetry of the 11D EFT.