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  On spinorial representations of involutory subalgebras of Kac-Moody algebras

Kleinschmidt, A., Nicolai, H., & Vigano, A. (in preparation). On spinorial representations of involutory subalgebras of Kac-Moody algebras.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0002-AF5C-3 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-EDDA-E
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 Creators:
Kleinschmidt, Axel1, Author              
Nicolai, Hermann2, Author              
Vigano, Adriano2, Author              
Affiliations:
1Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              
2Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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Free keywords: High Energy Physics - Theory, hep-th
 Abstract: The representation theory of involutory (or 'maximal compact') subalgebras of infinite-dimensional Kac-Moody algebras is largely terra incognita, especially with regard to fermionic (double-valued) representations. Nevertheless, certain distinguished such representations feature prominently in proposals of possible symmetries underlying M theory, both at the classical and the quantum level. Here we summarise recent efforts to study spinorial representations systematically, most notably for the case of the hyperbolic Kac-Moody algebra $E_{10}$ where spinors of the involutory subalgebra $K(E_{10})$ are expected to play a role in describing algebraically the fermionic sector of $D=11$ supergravity and M theory. Although these results remain very incomplete, they also point towards the beginning of a possible explanation of the fermion structure observed in the Standard Model of Particle Physics.

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 Dates: 2018-11-28
 Publication Status: Not specified
 Pages: 33 pages
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 Rev. Method: -
 Identifiers: arXiv: 1811.11659
URI: http://arxiv.org/abs/1811.11659
 Degree: -

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