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Minimal Unitary Realizations of Exceptional U-duality Groups and Their Subgroups as Quasiconformal Groups

M. Gunaydin·O. Pavlyk
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Abstract

We study the minimal unitary representations of noncompact exceptional groups that arise as U-duality groups in extended supergravity theories. First we give the unitary realizations of the exceptional group E_{8(-24)} in SU*(8) as well as SU(6,2) covariant bases. E_{8(-24)} has E_7 X SU(2) as its maximal compact subgroup and is the U-duality group of the exceptional supergravity theory in d=3. For the corresponding U-duality group E_{8(8)} of the maximal supergravity theory the minimal realization was given in hep-th/0109005. The minimal unitary realizations of all the lower rank noncompact exceptional groups can be obtained by truncation of those of E_{8(-24)} and E_{8(8)}. By further truncation one can obtain the minimal unitary realizations of all the groups of the "Magic Triangle". We give explicitly the minimal unitary realizations of the exceptional subgroups of E_{8(-24)} as well as other physically interesting subgroups. These minimal unitary realizations correspond, in general, to the quantization of their geometric actions as quasi-conformal groups as defined in hep-th/0008063.

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M. Gunaydin, O. Pavlyk. 2004-09-28. Minimal Unitary Realizations of Exceptional U-duality Groups and Their Subgroups as Quasiconformal Groups. https://doi.org/10.1088/1126-6708%2F2005%2F01%2F019

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