On the underlyingE₁₁symmetry of theD= 11 free differential algebra

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 Inönü-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 E 11 . This result suggests that the E 11 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.

Higher T-duality of super M-branes

“…That this 11d exceptional tangent bundle (46) happens to be the bosonic body of the D'Auria-Fré (DF) algebra R 10,1|32 exc,s (Def. 4.13, already due to [D'AF82]) has been highlighted in [Vau07]. However, it seems that no relation between the DF-algebra R 10,1|32 exc,s and the actual idea of M-theoretic generalized geometry promoted in [H07b, PW08, Bar12] has been observed before.…”

Super-exceptional geometry: origin of heterotic M-theory and super-exceptional embedding construction of M5

“…(ii) However, the actual meaning or role of this "hidden supergroup" had remained open; as it was not used for the re-derivation of D = 11 supergravity in [D'AF82], but discussed as an afterthought. In particular, the meaning or role of the extra fermion field required by super-exceptional spacetime had remained open [ADR16, p. 3] and the relation of the bosonic fields to exceptional M-geometry had remained unnoticed except in [Va07]…”

“…4,7]. Arguments were given in [Va07][Ba17] [FSS18][SS18] that the super-exceptional geometry for maximal n = 11 is to be identified with what was called the "hidden supergroup of 11d supergravity" in [D'AF82][BAIPV04] [ADR16], but open questions remained. In particular, the physical meaning of (a) the extra fermion field η on super-exceptional spacetime (see Def.…”

Expansions of Algebras and Superalgebras and Some Applications

“…3 can also be applied to the construction of Chern-Simons lagrangians [63]. The reduction of the D = 11 supergravity FDA has been very recently analyzed [64] in terms of the Sezgin algebra [11] and the E 11 Kac-Moody algebra.…”