E10 symmetry in one-dimensional supergravity

It has been known that D = 5 simple supergravity resembles D = 11 supergravity in many respects. We present their further resemblances in (1) the duality groups upon dimensional reduction, and (2) the worldsheet structure of the solitonic string of the D = 5 supergravity. We show that the D = 3, G 2(+2) /SO(4) (bosonic) nonlinear sigma model is obtained by using Freudenthal's construction in parallel to the derivation of the D = 3, E 8(+8) /SO(16) sigma model from D = 11 supergravity. The zero modes of the string solution with unbroken (4,0) supersymmetry consist of three (non-chiral) scalars, four Majorana-Weyl spinors of the same chirality and one chiral scalar, which suggests a duality to a certain six-dimensional chiral string theory. The worldsheet gravitational anomaly indicates a quantum correction to the Bianchi identity for the dualized two-form gauge field in the bulk just like the M5-brane case.

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“…The derivation is completely parallel to that of the D = 3, E 8(+8) /SO(16) sigma model from D = 11 supergravity [5].…”

Section: Introductionmentioning

confidence: 90%

More on the similarity between D=5 simple supergravity and M theory

1998

Self Cite

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“…Here, ǫ is a 32-dimensional spinor which, as an SO (10) representation, is a 32-component Majorana spinor of SO (10). Now it is straightforward to check from (2.26), by using Γ algebra, that the sufficient consistency condition (2.22) is satisfied.…”

Section: Serre-like Relations For K(e 10 )mentioning

confidence: 99%

“…Starting with the work of [2,3] the chain of exceptional symmetry groups E n (R) has been a recurring theme in analyses of these symmetry structures [4,5,6,7]. In particular, the emergence of the hyperbolic Kac-Moody algebra E 10 in the reduction to one dimension had already been conjectured in [8], see also [9,10]. More recently, it was argued that the bosonic supergravity field equations in eleven space-time dimensions correspond to a non-linear realization of the indefinite Kac-Moody group E 11 (jointly with the conformal group) [11,12], and these considerations were extended also to the (massive) IIA and IIB supergravity theories [13,14,15] by using the same groups.…”

Section: Introductionmentioning

confidence: 99%

K(E₁₀), supergravity and fermions

Damour¹,

Kleinschmidt²,

Nicolai³

2006

J. High Energy Phys.

212

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Abstract:We study the fermionic extension of the E 10 /K(E 10 ) coset model and its relation to eleven-dimensional supergravity. Finite-dimensional spinor representations of the compact subgroup K(E 10 ) of E 10 (R) are studied and the supergravity equations are rewritten using the resulting algebraic variables. The canonical bosonic and fermionic constraints are also analysed in this way, and the compatibility of supersymmetry with local K(E 10 ) is investigated. We find that all structures involving A 9 levels ℓ = 0, 1 and 2 nicely agree with expectations, and provide many non-trivial consistency checks of the existence of a supersymmetric extension of the E 10 /K(E 10 ) coset model, as well as a new derivation of the 'bosonic dictionary' between supergravity and coset variables. However, there are also definite discrepancies in some terms involving level ℓ = 3, which suggest the need for an extension of the model to infinite-dimensional faithful representations of the fermionic degrees of freedom.

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“…The IIB theory possess an SL(2, R) symmetry [4] while the IIA supergravity and IIB supergravity dimensionally reduced on an (n − 1)-torus, or equivalently the eleven-dimensional supergravity theory on an n-torus, possess an E n symmetry for n = 7, 8, 9 [8,9,10] and possibly n = 10 [11]. For other work on symmetries that appear in dimensional reduction see [12][13][14][15][16][17][18] and we note that the E n symmetries necessarily contain T -duality which is a perturbative symmetry of string theory [19,20] . These theories possess charged states which are rotated by these symmetries and their charges obey the quantization condition [21].…”

Section: ½º áòøöó ùø óòmentioning

confidence: 99%