MAXIMAL SUPERGRAVITIES AND THE E₁₀ COSET MODEL

Abstract

The maximal rank hyperbolic Kac-Moody algebra e 10 has been conjectured to play a prominent role in the unification of duality symmetries in string and M-theory. We review some recent developments supporting this conjecture.

Complexity and the Big Bang

“…These difficulties multiply as one probes degrees of freedom beyond the CSA. Nevertheless, with only the Iwasawa gauge to rely on, exploiting local K(E 10 ) symmetry to restrict the degrees of freedom to non-negative levels in (7), one can show that the different maximal supergravities with their duality symmetries all emerge at low levels, depending on how one 'slices' e 10 in (7) [27,28,29]. Still, no investigation has gone beyond |ℓ| ≤ 4 so far, despite many efforts.…”

Arithmetic Quantum Gravity

“…The BKL-type expansion of the dynamics in terms of spatial gradients near the singularity is converted into a "level expansion" of the infinite dimensional E 10 Lie algebra defining the coset model, and the general validity of this conjecture has been confirmed for various maximal supergravities at low levels. 22 This provides a purely algebraic reformulation of geometric concepts in what could be termed a "pre-geometrical" scheme. The full Hamiltonian of the E 10 /K(E 10 ) model is the unique Casimir operator of E 10…”

E10: Eine fundamentale Symmetrie der Physik? Neuer Zugang zur Quantengravitation

“…Stattdessen ist hier die algebraische E10-Sichtweise angemessen: Sie liefert eine mögliche Beschreibung der Physik im Bereich der Planck-Skala. Bevor wir uns den Konsequenzen dieser Sichtweise für die Quantengravitation zuwenden, diskutieren wir noch einige klassische Aspekte des E10-Modells [8].…”