M-theory and E10: Billiards, Branes, and Imaginary Roots

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Eleven dimensional supergravity compactified on $T^10$ admits classical solutions describing what is known as billiard cosmology - a dynamics expressible as an abstract (billiard) ball moving in the 10-dimensional root space of the infinite dimensional Lie algebra E10, occasionally bouncing off walls in that space. Unlike finite dimensional Lie algebras, E10 has negative and zero norm roots, in addition to the positive norm roots. The walls above are related to physical fluxes that, in turn, are related to positive norm roots (called real roots) of E10. We propose that zero and negative norm roots, called imaginary roots, are related to ... continued below

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Brown, Jeffrey; Ganor, Ori J. & Helfgott, Craig January 9, 2004.

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Eleven dimensional supergravity compactified on $T^10$ admits classical solutions describing what is known as billiard cosmology - a dynamics expressible as an abstract (billiard) ball moving in the 10-dimensional root space of the infinite dimensional Lie algebra E10, occasionally bouncing off walls in that space. Unlike finite dimensional Lie algebras, E10 has negative and zero norm roots, in addition to the positive norm roots. The walls above are related to physical fluxes that, in turn, are related to positive norm roots (called real roots) of E10. We propose that zero and negative norm roots, called imaginary roots, are related to physical branes. Adding 'matter' to the billiard cosmology corresponds to adding potential terms associated to imaginary roots. The, as yet, mysterious relation between E10 and M-theory on $T^10$ can now be expanded as follows: real roots correspond to fluxes or instantons, and imaginary roots correspond to particles and branes (in the cases we checked). Interactions between fluxes and branes and between branes and branes are classified according to the inner product of the corresponding roots (again in the cases we checked). We conclude with a discussion of an effective Hamiltonian description that captures some features of M-theory on $T^10.$

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  • Journal Name: Journal of High Energy Physics; Related Information: Journal Publication Date: 7 October 2004

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  • Report No.: LBNL-54228
  • Grant Number: DE-AC02-05CH11231
  • DOI: 10.1088/1126-6708/2004/08/063 | External Link
  • Office of Scientific & Technical Information Report Number: 965363
  • Archival Resource Key: ark:/67531/metadc931333

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  • January 9, 2004

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  • Nov. 13, 2016, 7:26 p.m.

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  • Nov. 18, 2016, 2:55 p.m.

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Brown, Jeffrey; Ganor, Ori J. & Helfgott, Craig. M-theory and E10: Billiards, Branes, and Imaginary Roots, article, January 9, 2004; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc931333/: accessed September 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.