Abstract
Recently proposed exceptional field theories (EFTs) making manifest the duality En(n) symmetry, first observed as nonlinearly realized symmetries of the maximal d=3,4,...,9 supergravity (n=11−d) and containing 11D and type IIB supergravity as sectors, were formulated in enlarged spacetimes. In the case of E7(7) EFT such an enlarged spacetime can be identified with the bosonic body of the d=4 central charge superspace Σ(60|32), the N=8d=4 superspace completed by 56 additional bosonic coordinates associated to central charges of the maximal d=4 supersymmetry algebra.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.
Highlights
The natural question is: are there more underlying EFT (uEFT) superparticle models? we present the family of superparticle models in Σ(528|32) superspace, first described in [77], and show that each of these generates a constraint solving the classical section conditions (3.10), (3.11) of the hypothetical 11D exceptional field theories (EFTs)
In this paper we conjectured the existence of hypothetical underlying exceptional field theory, which we abbreviated as 11D EFT or uEFT, defined in the maximal tensorial central charge superspace
We have presented some arguments in favor of this conjecture, based on the hypothesis that the additional coordinates of all the En(n) EFTs with n ≤ 8 should be related to the maximally extended d = 11− n dimensional supersymmetry algebra, and have proposed the candidate section conditions for this hypothetical uEFT
Summary
{Qαi, Qβj } = ǫαβ ̇ Zij , α , β = 1, 2 , a = 0, 1, 2, 3 , i, j = 1, ..., 8 This observation allowed us [67] to formulate a superparticle model in central charge superspace which generates the classical counterpart of the independent section conditions (2.9) as a constraint. For our discussion here the presence of even more (’beyond the E8(8) EFT’) additional coordinates is not problematic but rather suggestive At this stage it is tempting to conjecture the existence of an underlying exceptional field theory (uEFT), which includes as a sub-sectors all the En(n) EFT with 2 ≤ n ≤ 8 and lives in an enlarged superspace Σ(528|32) with 32 fermionic and 528 bosonic coordinates. We present the possible section conditions of the hypothetical 11D EFT
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