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Motivated by the recent analysis of the E10 sigma model for the study of Mtheory, we study a one-dimensional sigma model associated with the hyperbolicKac-Moody algebra G2H and its link to D=5, N=2 pure supergravity, which closelyresembles in many ways D=11 supergravity. The bosonic equations of motion andthe Bianchi identity for D=5 pure supergravity match the equations of the levell<=3 truncation of the G2H sigma model up to higher level terms, just as theydo for the D=11 case. We also compute low level root and outer multiplicitiesin 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 atl =4 remains a puzzle.Comment: 18 pages, 1 figur

Five-dimensional supergravity and the hyperbolic Kac–Moody algebra G H 2

Five-dimensional supergravity and the hyperbolic Kac–Moody algebra G ^H ₂