On the underlying E11 symmetry of the D=11 Free Differential Algebra

TL;DR

This paper demonstrates that the D=11 supergravity's Free Differential Algebra can be reduced to known algebraic structures, revealing underlying E11 symmetries that are encoded in the FDA and become explicit on an enlarged group manifold.

Contribution

It shows the reduction of the D=11 supergravity FDA to E11 and M-Algebra, connecting these symmetries to the algebraic structure of the FDA.

Findings

FDA reduces to M-Algebra in flat background with zero three-form

FDA reduces to E11 at lowest levels with non-trivial three-form

E11 symmetries are encoded in the D=11 FDA and explicit on enlarged manifolds

Abstract

We study the reduction of the Free Differential Algebra (FDA) of D=11 supergravity to an ordinary algebra. We show that in flat background and with vanishing three-form field strength, the corresponding minimal FDA can be reduced to an Inonu-Wigner contraction of Sezgin's M-Algebra. We also prove that in flat background but with a non trivial three-form field strength, the bosonic FDA can be reduced to the lowest levels of E11. This result suggests that the E11 symmetries, which act on perturbative states as well, are already encoded in the D=11 FDA and are made explicit when the theory is formulated on a enlarged group manifold.