Conformal and Quasiconformal Realizations of Exceptional Lie Groups

Günaydin, Murat; Koepsell, Kilian; Nicolai, Hermann

doi:10.1007/PL00005574

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Conformal and Quasiconformal Realizations of Exceptional Lie Groups

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Koepsell, Kilian
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Nicolai, Hermann
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Günaydin, M., Koepsell, K., & Nicolai, H. (2001). Conformal and Quasiconformal Realizations of Exceptional Lie Groups. Communications in Mathematical Physics, 221(1), 57-76. doi:10.1007/PL00005574.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-55F9-9

Abstract

We present a nonlinear realization of E_8 on a space of 57 dimensions, which is quasiconformal in the sense that it leaves invariant a suitably defined ''light cone'' in 57 dimensions. This realization, which is related to the Freudenthal triple system associated with the unique exceptional Jordan algebra over the split octonions, contains previous conformal realizations of the lower rank exceptional Lie groups on generalized space times, and in particular a conformal realization of E_7 on a 27 dimensional vector space which we exhibit explicitly. Possible applications of our results to supergravity and M-Theory are briefly mentioned.