G+++ Invariant Formulation of Gravity and M-Theories: Exact BPS Solutions

F. Englert; L. Houart

doi:10.1088/1126-6708/2004/01/002

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arXiv · hep-th/0311255

G+++ Invariant Formulation of Gravity and M-Theories: Exact BPS Solutions

F. Englert·L. Houart

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Abstract

We present a tentative formulation of theories of gravity with suitable matter content, including in particular pure gravity in D dimensions, the bosonic effective actions of M-theory and of the bosonic string, in terms of actions invariant under very-extended Kac-Moody algebras G+++. We conjecture that they host additional degrees of freedom not contained in the conventional theories. The actions are constructed in a recursive way from a level expansion for all very-extended algebras G+++. They constitute non-linear realisations on cosets, a priori unrelated to space-time, obtained from a modified Chevalley involution. Exact solutions are found for all G+++. They describe the algebraic properties of BPS extremal branes, Kaluza-Klein waves and Kaluza-Klein monopoles. They illustrate the generalisation to all G+++ invariant theories of the well-known duality properties of string theories by expressing duality as Weyl invariance in G+++. Space-time is expected to be generated dynamically. In the level decomposition of E8+++ = E11, one may indeed select an A10 representation of generators Pa which appears to engender space-time translations by inducing infinite towers of fields interpretable as field derivatives in space and time.

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F. Englert, L. Houart. 2003-12-15. G+++ Invariant Formulation of Gravity and M-Theories: Exact BPS Solutions. https://doi.org/10.1088/1126-6708%2F2004%2F01%2F002

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