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Real forms of very extended Kac-Moody algebras and theories with eight supersymmetries
High Energy Physics - Theory · Submitted 17 Jan 2008
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show for the most interesting cases that the bosonic sector of the supersymmetric theory is precisely reproduced by the corresponding non-linear realisation.
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The abstract, sentence by sentence
We consider all theories with eight supersymmetries whose reduction to three dimensions gives rise to scalars that parametrise symmetric manifolds. We conjecture that these theories are non-linear realisations of very-extended Kac-Moody algebras for suitable choices of real forms. We show for the most interesting cases that the bosonic sector of the supersymmetric theory is precisely reproduced by the corresponding non-linear realisation.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We consider all theories with eight supersymmetries whose reduction to three dimensions gives rise to scalars that parametrise symmetric manifolds. | contribution 0.61 | 0.52 | 0.04 | asserted 0.73 |
| s1 | We conjecture that these theories are non-linear realisations of very-extended Kac-Moody algebras for suitable choices of real forms. | contribution 0.62 | 0.37 | 0.36 | speculative 1.00 |
| s2 | We show for the most interesting cases that the bosonic sector of the supersymmetric theory is precisely reproduced by the corresponding non-linear realisation. | result 0.99 | 0.95 | 0.66 | asserted 1.00 |
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The paper
Original abstract
We consider all theories with eight supersymmetries whose reduction to three dimensions gives rise to scalars that parametrise symmetric manifolds. We conjecture that these theories are non-linear realisations of very-extended Kac-Moody algebras for suitable choices of real forms. We show for the most interesting cases that the bosonic sector of the supersymmetric theory is precisely reproduced by the corresponding non-linear realisation.
Human review
How the literature uses it
16 arXiv papers cite this in 28 sentences
Papers citing it · 23 sentences without a confident label
Builds on it 1 paper
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The same applies to all supergravity theories with more than 16 supercharges [ref] .
The very-extended trombone · Conclusions · 0.80
Cites it as background 4 papers
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This results in very special real forms of Kac-Moody algebras that have not been discussed fully in the literature before (see, however, [ref] for the general theory and [ref] for some special cases and low level field content).
Real forms of extended Kac-Moody symmetries and higher spin gauge theories · Introduction · 0.86
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This can be found in e.g. [ref] .
Extended Symmetries in Supergravity: the Semi-simple Case · Very-extended $_2 ⊕(2)$ and the pure theory · 0.91
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The multiplets of maximal supergravity in five and six dimensions derived from $n$ and $n-1$ forms have been found using $E_11$ in [ref] and using the very extension of real forms of $E_8$ in [ref] .
Off-Shell Hodge Dualities in Linearised Gravity and E11 · Maximal Supergravity, Dual Gravity and $E_11$ · 0.82
What it cites · 34 sentences without a confident label
Uses the method or tool of 2 papers
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The fields at the next levels can be found using the decomposition techniques of reference [ref] .
E_{11} origin of Brane charges and U-duality multiplets · $D_P2+4(4)^+++$ and $L(0,P)$, $P$ even · 1.00
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One can calculate the representations found in this appendix using the programme SimpLie [ref] .
E(11) and the Embedding Tensor · The Calculation of the Form Fields · 0.99
Uses data or values from 3 papers
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Here $D_q+1$ is the dimension of the irreducible representation of the Clifford algebra in $q+1$ dimensions with positive signature, and takes the values $D_q+1=1 for q=-1,0$, $D_q+1=2 for q=1$, $D_q+1=4 for q=2$, $D_q+1=8 for q=3,4$, $D_q+1=16 for q=5,,6,7,8$ and $D_q+8=16D_q$ [ref] .
Tits-Satake projections of homogeneous special geometries · Review of theories with eight supersymmetries · 0.81
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Here $D_q+1$ is the dimension of the irreducible representation of the Clifford algebra in $q+1$ dimensions with positive signature, and takes the values $D_q+1=1 for q=-1,0$, $D_q+1=2 for q=1$, $D_q+1=4 for q=2$, $D_q+1=8 for q=3,4$, $D_q+1=16 for q=5,,6,7,8$ and $D_q+8=16D_q$ [ref] .
Special geometry, cubic polynomials and homogeneous quaternionic spaces · Review of theories with eight supersymmetries · 0.81
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Since $α^2 =2,0.-2,…$ it is straightforward to find solutions to this equation once we know the possible scalar products of the fundamental weights which for $E_n, n=6,7,8$ are given by [ref] [equation] and [equation] and [equation]
E_{11} origin of Brane charges and U-duality multiplets · The Calculation of the Form Fields · 0.88
Compares with 1 paper
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This is very similar to the situation of the well known IIA and IIB theories in ten dimensions and the way they fit into $E_8^+++$ [ref] giving rise to a unique nine dimensional theory upon dimensional reduction.
Kac-Moody Symmetries of IIB Supergravity · $D_P2+4(4)^+++$ and $L(0,P)$, $P$ even · 0.85
Cites as background 20 papers
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It was proposed that the bosonic string effective action generalised to $D$ dimensions is associated with the non-linear realisation of an algebra originally denoted by $K_27$ in the 26-dimensional case and which was later identified with $D_D-2^+++$ [ref] , and similarly gravity in $D$ dimensions is associated with $A_D-3^+++$ [ref] .
Coset Symmetries in Dimensionally Reduced Bosonic String Theory · Introduction · 0.86
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It was proposed that the bosonic string effective action generalised to $D$ dimensions is associated with the non-linear realisation of an algebra originally denoted by $K_27$ in the 26-dimensional case and which was later identified with $D_D-2^+++$ [ref] , and similarly gravity in $D$ dimensions is associated with $A_D-3^+++$ [ref] .
E_11 and M Theory · Introduction · 0.86
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The original $E_11$ conjecture [ref] concerned the eleven dimensional supergravity theory, the ten dimensional IIA and IIB supergravity theories [ref] and their dimensional reductions.
Kac-Moody Symmetries of IIB Supergravity · Introduction · 0.98
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