Conformal and Quasiconformal Realizations of Exceptional Lie Groups

TL;DR

This paper constructs a nonlinear quasiconformal realization of the exceptional Lie group E_8 in 57 dimensions, extending previous conformal realizations of lower-rank groups, with potential implications for supergravity and M-Theory.

Contribution

It introduces a novel quasiconformal realization of E_8 linked to the Freudenthal triple system, expanding the understanding of exceptional Lie groups in higher dimensions.

Findings

Realization of E_8 on a 57-dimensional space.

Explicit conformal realization of E_7 on 27-dimensional space.

Potential applications to supergravity and M-Theory.

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.