The structure of E10 at higher A9 levels - a first algorithmic approach

Abstract

The conjecture of a hidden $E_{10}$ symmetry of M-theory is supported by the close connection between the dynamics of D=11 supergravity near a spacelike singularity and a truncation of an one-dimensional $\sigma$-model with $E_{10}$ symmetry where all representations beyond SL(10) level $\ell =3$ are omitted. If this conjecture is right, higher-level representations should especially capture the dynamics of further M-theory degrees of freedom. Unfortunately, the level by level determination of $E_{10}$ commutators which is necessary to extend the model to higher levels is both an involved and toilsome task that requires computer aid. In this work, some of the relevant problems are exposed and algorithmic methods are developed which simplify key steps in the determination of explicit $E_{10}$ commutators at higher levels. As an application, we compute the commutator of the level-two six-form with itself.

26 pages, 1 figure

References in corpus (5)

• E10 and SO(9,9) invariant supergravity
• Higher order M theory corrections and the Kac-Moody algebra E10
• IIB supergravity and E10
• Eleven dimensional supergravity and the E10/KE10 sigma-model at low A9 levels
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Cited by in corpus (7)

• Spacelike Singularities and Hidden Symmetries of Gravity
• Extended E8 Invariance of 11-Dimensional Supergravity
• K(E10), Supergravity and Fermions
• Gradient Representations and Affine Structures in AE(n)
• On the E10/Massive Type IIA Supergravity Correspondence
• Arithmetic and Hyperbolic Structures in String Theory
• Hidden Borcherds symmetries in Z_n orbifolds of M-theory and magnetized D-branes in type 0' orientifolds