Z_N-Invariant Subgroups of Semi-Simple Lie Groups

M. K. Ahsan; T. Hubsch

Z_N-Invariant Subgroups of Semi-Simple Lie Groups

High Energy Physics - Theory 2017-06-20 v2 Mathematical Physics math.MP

Authors: M. K. Ahsan , T. Hubsch

Abstract

We employ Mathematica to find $Z_N$ -invariant subgroups of $E_8$ for application in M-theory. These $Z_N$ -invariant subgroups are phenomenologically important and in some cases they resemble the gauge groups of our real world. We present a specific example of $Z_7$ -invariant subgroups of $E_8$ , which turn up in orbifold compactification of M-theory. Moreover, the procedure can be applied for any $Z_N$ group that acts by shifts (translations) in the root lattice of semisimple Lie groups with $A_n,B_n,C_n,D_n,E_6,E_7$ and $E_8$ factors.

Keywords

Z_N-invariant subgroups E_8 M-theory orbifold compactification semi-simple lie groups root lattice

Cite

@article{arxiv.1003.5823,
  title  = {Z_N-Invariant Subgroups of Semi-Simple Lie Groups},
  author = {M. K. Ahsan and T. Hubsch},
  journal= {arXiv preprint arXiv:1003.5823},
  year   = {2017}
}

Comments

Update reflects some corrections and streamlined results hastened by the journal Referee; LaTeX 3 times for correct "longtable" processing

Z_N-Invariant Subgroups of Semi-Simple Lie Groups

Abstract

Keywords

Cite

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