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

Abstract

Recently proposed exceptional field theories (EFTs) making manifest the duality E n(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 E 7(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 = 8 d = 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 E n(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 E n(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.symmetries are the exceptional Lie groups from the Cartan list, for lower n E n(n) denote simpler groups: E 5(5) = SO(5, 5), E 4(4) = SL(5), E 3(3) = SL(2) × SL(2) and, as it was proposed in recent [18], E 2(2) = SL(2) × R + .3 See [32] and refs. therein for T-duality and [33,34,35,36,37,31,38,39,40] for string and superstring in doubled (super)spaces. Notice also that we usually denote the number of spacetime dimensions by D when it is equal to 10 or 11, and by d when it is lower, so that d ≤ 9.4 The name 'section conditions' was introduced in [4] developing E 4(4) = SL(5) (pre-)EFT formalism of [41]. The name EFT was introduced in [1] which starts a series of papers formulating the EFTs for exceptional U-duality groups E7,7, E 6(6) and E 8(8) in its complete form, including all the differential form fields of maximal d = 11 − n dimensional supergravity. 5 Notice a partial intersection of (the 'left hand side' of) this Table 1 with Table 2 of [42], where a possible relation of 11D supermembrane duality transformations with E n(n) duality symmetries of dimensionally reduced maximal supergravity was discussed.

Higher Spin Fields in Hyperspace. A Review

“…From (134), it then follows that the conventional conformal weight ∆ D of the scalar superfield is related to the generalized one ∆ via…”

“…This similarity can be relevant for higher-spin extensions of these theories, provided the section conditions can be properly relaxed (see e.g., [133,134] for a discussion of this point). It would be interesting to further elaborate on this issue, as a connection to the E 11 framework [18].…”

η-symbols in exceptional field theory

“…By using the obtained η-symbols, the section condition η IJ; I ∂ I ⊗ ∂ J = 0 can be expressed as follows (see [22] for a quite similar section condition and also [25] for a section condition in the "underlying EFT"):…”

“…Under the section condition, all fields can depend on at most d coordinates (see [24] for a proof in the E 7(7) EFT).In the above conventional formulation, the Y -tensor and the section condition strongly depend on the dimension d, and when we consider applications of the E d(d) EFT, we need to specify the dimension d explicitly. A hypothetical "underlying EFT" (or 11D EFT), which reproduces all E d(d) EFTs (d ≤ 8) from simple truncations, has been proposed in [25], but the program has not been completed yet. In this paper, we investigate such uniform formulations from a different approach.…”

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

“…The Kaluza-Klein (KK) compactifications of 11d supergravity on n-tori have a rich space of scalar moduli fields invariant under ever larger exceptional Lie groups as n increases [CJ79], reflecting just the expected duality symmetries acting on the corresponding string theories [HT95]. This led to the proposal [Hul07] (see also [KNS00][We03][PW08][We11] [Ba17]) that M-theory is an enhancement of D = 11 supergravity to a theory of "exceptional geometry" with a "generalized tangent bundle" of the form T ex X n exceptional tangent bundle := T X n ⊕ ∧ 2 X T * X n M2 wrapping modes ⊕ ∧ 5 X T * X n M5 wrapping modes ⊕ · · · (1) locally encoding wrapping modes of the M2-and the M5-brane already before KK-compactification.…”