Conformal and Quasiconformal Realizations of Exceptional Lie Groups

Details Conformal and Quasiconformal Realizations of Exceptional Lie Groups Conformal and Quasiconformal Realizations of Exceptional Lie Groups

2000-08-07

arxiv.org/abs/hep-th/0008063v2

Commun.Math.Phys.221:57-76,2001

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, 1 figure. Revised version. Connection between SU(8) and SL(8,R) bases clarified; formulas corrected; references adde

Scientific paper

10.1007/PL00005574

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.

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