Five-dimensional Supergravity and Hyperbolic Kac-moody

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 G2 and its link to D = 5, N = 2 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 G2 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 ER terms, although the missing singlet at l = 4 remains a puzzle.