E8 generators as bilinear fermions and its maximal subgroups

Mehmet Koca

doi:10.1103/PhysRevD.24.2645

E8 generators as bilinear fermions and its maximal subgroups

Mehmet Koca^*

^*Corresponding author for this work

Physics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

E8 algebra constructed as bilinear fermions in the bases of SU(9) and [SU(3)]4 is used to obtain the generators in the bases of the maximal subgroups SO(16), E7×SU(2), and SU(5)×SU(5). The representation of the generators in the Tits subgroup F4×G2 is also obtained using the [SU(3)]4 basis. Simple methods are developed to go from one basis to the other bases. Generators of the exceptional subgroups E7, E6, and F4 are decomposed with respect to their respective Tits subgroups SP(6)×G2, SU(3)×G2, and SO(3)×G2. The possible roles of these subgroups in the symmetry breaking of E8 are merely indicated.

Original language	English
Pages (from-to)	2645-2653
Number of pages	9
Journal	Physical review D
Volume	24
Issue number	10
DOIs	https://doi.org/10.1103/PhysRevD.24.2645
Publication status	Published - 1981

ASJC Scopus subject areas

Physics and Astronomy (miscellaneous)

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author = "Mehmet Koca",

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AB - E8 algebra constructed as bilinear fermions in the bases of SU(9) and [SU(3)]4 is used to obtain the generators in the bases of the maximal subgroups SO(16), E7×SU(2), and SU(5)×SU(5). The representation of the generators in the Tits subgroup F4×G2 is also obtained using the [SU(3)]4 basis. Simple methods are developed to go from one basis to the other bases. Generators of the exceptional subgroups E7, E6, and F4 are decomposed with respect to their respective Tits subgroups SP(6)×G2, SU(3)×G2, and SO(3)×G2. The possible roles of these subgroups in the symmetry breaking of E8 are merely indicated.

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E8 generators as bilinear fermions and its maximal subgroups

Abstract

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