Five-dimensional Supergravity and Hyperbolic Kac-Moody Algebra G2H

TL;DR

This paper explores the connection between a one-dimensional sigma model based on the hyperbolic Kac-Moody algebra G2H and five-dimensional N=2 supergravity, revealing structural similarities and computational insights into their equations of motion.

Contribution

It establishes a link between the G2H sigma model and D=5, N=2 supergravity, extending previous analyses from D=11 supergravity and computing root multiplicities.

Findings

Matching of equations of motion up to level l<=3

Identification of singlets at levels 4k, 2,3

Remaining puzzle at level 4 singlet

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 G2H 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 G2H 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^{k+1} terms, although the missing singlet at l =4 remains a puzzle.