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mitchell porter

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https://arxiv.org/abs/2005.03048

**Exceptional Unification of Families and Forces**

Alfredo Aranda, Francisco J. de Anda, Stephen F. King

*[Submitted on 6 May 2020]*

This work considers the remarkable suggestion that the three families of quarks and leptons may be unified, together with the Higgs and gauge fields of the Standard Model (SM), into a single "particle", namely the 248 vector superfield of a ten-dimensional E8 super Yang Mills (SYM) theory. Towards a realistic model along these lines, a class of orbifoldings based on T6/(ZN×ZM) are proposed and explored, that can in principle break E8 SYM down to the minimal supersymmetric standard model (MSSM), embedded in a larger group such as E6, SO(10) or SU(5), together with other gauge group factors which can be broken by Wilson lines. A realistic model based on T6/(Z6×Z4) is presented. The orbifold breaks E8 SYM down to a Pati-Salam gauge group in 4d, together with other gauge groups, which are further broken to the SM by Wilson lines in the flavon and right-handed sneutrino directions, yielding proto-realistic fermion mass matrices, and experimental signals associated with a low Pati-Salam gauge group breaking scale.

In grand unification, one usually only considers E6 but not E7 or E8, because the latter groups only have real representations, which leads to problems in obtaining the chiral fermions of the real world. String theory unification often starts e.g. from E8xE8, but there are stringy methods which allow one to obtain complex representations of the E6 in one of the E8s after all.

However, there is a neat way to single out Standard-Model-like particles from within the N=1 supersymmetric E8 multiplet, and so model builders are occasionally tempted to seek ways around the chiral problem, e.g. Stephen Adler's attempt.

In the current paper, the novelty is to use higher dimensions. Not a string theory, but a higher-dimensional N=1 E8 field theory that is then compactified and orbifolded.

For purposes of comparison, I would also call attention to Lubos Motl's reflections on whether the idea of breaking E8 into E6 times a flavor SU(3), could be realized within string theory after all.