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Research Article Open Access

On ZN-Invariant Subgroups of Semi-Simple Lie Groups


We employ Mathematica to find ZN-invariant subgroups of E8 for application in M-theory. These ZN-invariant subgroups are phenomenologically important and in some cases they resemble the gauge groups of our real world. We present a specific example of ZN-invariant subgroups of E8, which turn up in orbifold compactification of M-theory. However, the procedure can be applied for any ZN group that acts by shifts (translations) in the root lattice of semisimple Lie groups with An, Bn, Cn, Dn, E6, E7 and E8 factors.

Ahsan MK* and Hubsch T

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