On Chern–Simons (super) gravity, E8 Yang–Mills and polyvector-valued gauge theories in Clifford spaces

Abstract

It is shown how the E8 Yang–Mills theory is a small sector of a Cl(16) algebra gauge theory and why the 11D Chern–Simons (super) gravity theory can be embedded into a Cl(11) algebra gauge theory. These results may shed some light into the origins behind the hidden E8 symmetry of 11D supergravity. To finalize, we explain how the Clifford algebra gauge theory (that contains the Chern–Simons gravity action in D=11, for example) can itself be embedded into a more fundamental polyvector-valued gauge theory in Clifford spaces involving tensorial coordinates xμ1μ2,xμ1μ2μ3,…,xμ1μ2…μD in addition to antisymmetric tensor gauge fields Aμ1μ2,Aμ1μ2μ3,…,Aμ1μ2…μD. The polyvector-valued supersymmetric extension of this polyvector valued bosonic gauge theory in Clifford spaces may reveal more important features of a Clifford-algebraic structure underlying M, F theory.