E_{10} Symmetry in One-dimensional Supergravity

Shun'ya Mizoguchi (KEK Tanashi)

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E_{10} Symmetry in One-dimensional Supergravity

High Energy Physics - Theory · Submitted 24 Mar 1997

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We further show that an extra $SL(2,R)$ symmetry, which is newly present upon reduction to one dimension, extends the symmetry algebra to a real form of $E_{10}$.

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What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.25 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.34 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; show every role.

We consider dimensional reduction of the eleven-dimensional supergravity to less than four dimensions. The three-dimensional $E_{8(+8)}/SO(16)$ nonlinear sigma model is derived by direct dimensional reduction from eleven dimensions. In two dimensions we explicitly check that the Matzner-Misner-type $SL(2,R)$ symmetry, together with the $E_8$, satisfies the generating relations of $E_9$ under the generalized Geroch compatibility (hypersurface-orthogonality) condition. We further show that an extra $SL(2,R)$ symmetry, which is newly present upon reduction to one dimension, extends the symmetry algebra to a real form of $E_{10}$. The new $SL(2,R)$ acts on certain plane wave solutions propagating at the speed of light. To show that this $SL(2,R)$ cannot be expressed in terms of the old $E_9$ but truly enlarges the symmetry, we compactify the final two dimensions on a two-torus and confirm that it changes the conformal structure of this two-torus.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We consider dimensional reduction of the eleven-dimensional supergravity to less than four dimensions.	background 0.48	0.64	0.02	asserted 0.67
s1	The three-dimensional $E_{8(+8)}/SO(16)$ nonlinear sigma model is derived by direct dimensional reduction from eleven dimensions.	result 0.88	0.88	0.06	asserted 1.00
s2	In two dimensions we explicitly check that the Matzner-Misner-type $SL(2,R)$ symmetry, together with the $E_8$, satisfies the generating relations of $E_9$ under the generalized Geroch compatibility (hypersurface-orthogonality) condition.	result 0.81	0.90	0.06	asserted 1.00
s3	We further show that an extra $SL(2,R)$ symmetry, which is newly present upon reduction to one dimension, extends the symmetry algebra to a real form of $E_{10}$.	result 0.93	0.95	0.83	asserted 1.00
s4	The new $SL(2,R)$ acts on certain plane wave solutions propagating at the speed of light.	result 0.88	0.75	0.05	asserted 1.00
s5	To show that this $SL(2,R)$ cannot be expressed in terms of the old $E_9$ but truly enlarges the symmetry, we compactify the final two dimensions on a two-torus and confirm that it changes the conformal structure of this two-torus.	method 0.50	0.94	0.11	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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The paper

Original abstract

We consider dimensional reduction of the eleven-dimensional supergravity to less than four dimensions. The three-dimensional $E_{8(+8)}/SO(16)$ nonlinear sigma model is derived by direct dimensional reduction from eleven dimensions. In two dimensions we explicitly check that the Matzner-Misner-type $SL(2,R)$ symmetry, together with the $E_8$, satisfies the generating relations of $E_9$ under the generalized Geroch compatibility (hypersurface-orthogonality) condition. We further show that an extra $SL(2,R)$ symmetry, which is newly present upon reduction to one dimension, extends the symmetry algebra to a real form of $E_{10}$. The new $SL(2,R)$ acts on certain plane wave solutions propagating at the speed of light. To show that this $SL(2,R)$ cannot be expressed in terms of the old $E_9$ but truly enlarges the symmetry, we compactify the final two dimensions on a two-torus and confirm that it changes the conformal structure of this two-torus.

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References

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

$E_{d(d)} \times \mathbb{R}^+$ Generalised Geometry, Connections and M theory
hep-th 2011-12 accept novelty 7.0 of 10

The bosonic action and equations of motion of restricted eleven-dimensional supergravity are exactly the Ricci scalar and vanishing Ricci tensor of a generalised geometry with E_{d(d)} x R+ symmetry.
Enhanced Coset Symmetries and Higher Derivative Corrections
hep-th 2006-03 conditional novelty 7.0 of 10

Dimensional reduction of gravity, M-theory, and the bosonic string to three dimensions produces higher derivative coefficients that are weights of the enhanced symmetry group, with weights appearing only for selected ...
Dualisation of Dualities, I
hep-th 1997-10 accept novelty 6.0 of 10

The global symmetry of a compactified supergravity depends on which fields are dualised, and the resulting symmetry groups correspond to deleting positive roots from the maximal duality algebra.
Exceptional Periodicity and Magic Star Algebras. I : Foundations
math.RT 2019-09 conditional novelty 5.0 of 10

The paper rigorously defines 'Magic Star algebras', periodic finite dimensional generalizations of e6, e7, and e8, which are Lie algebras only at the base level n=1.

How the literature uses it

5 arXiv papers cite this in 5 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Cites it as background 3 papers

The hidden symmetry algebra was more generally conjectured to be $E_11-D$ for maximal supergravity reduced to $D$ dimensions [ref] , which implied reaching the affine Kac-Moody algebra $E_9$ in $D=2$ [ref] , and, possibly, the hyperbolic Kac-Moody algebra $E_10$ when reducing to one timelike direction [ref] .

Hidden Kac-Moody Structures in the Fermionic Sector of Five-Dimensional Supergravity · Introduction · 0.94
Prior to this $𝔢_10$ was shown to be a symmetry of bosonic supergravity dimensionally reduced to one dimension [ref] .

Bound States of String Theory and Beyond · Introduction · 0.83
Similar results hold in various other theories of gravity: $D$-dimensional vacuum gravity has an $SL(D-2,ℝ)$ symmetry [ref] ; $4$-dimensional Einstein-Maxwell gravity has an $SU(2,1)$ symmetry [ref] ; $5$-dimensional minimal supergravity has a $G_2(2)$ symmetry [ref] ; $11$-dimensional supergravity has an $E_8(8)$ symmetry [ref] .

Five-dimensional electrostatic black holes in a background field · Introduction · 0.80

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