Five-dimensional supergravity and the hyperbolic Kac–Moody algebra GH2

Abstract

Motivated by the recent analysis of the E10 sigma model for the study of M-theory, we study a one-dimensional sigma model associated with the hyperbolic Kac–Moody algebra GH2 and its link to pure supergravity, which closely resembles in many ways D = 11 supergravity. The bosonic equations of motion and the Bianchi identity for D = 5 pure supergravity match the equations of the level ℓ ⩽ 3 truncation of the GH2 sigma model up to higher level terms, just as they do for the D = 11 case. We also compute low level root and outer multiplicities in the A3 decomposition, and indeed find singlets at ℓ = 4k, k = 2, 3, … corresponding to the scaling of ERk+1 terms, although the missing singlet at ℓ = 4 remains a puzzle.