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After left-right symmetry extension of the standard model, $$G' \times SU(2)^L \times SU(2)^R$$ it would seem that a logical pathway to grand unification is to try to obtain it by breaking down from two copies of the same group, $$G^L \times G^R$$ I think to remember such "GxG" possibility mentioned in old reviews of grand unification, but not pursued. Now, was there some deep motivation to do not follow this path, or it was only the point that it seems to avoid the opportunity to rule out some groups (as we can not use the complex vs real representations argument anymore)? Because if it were the later, I had expected some revival after the discovery of $E_8 \times E_8$, but I can not finy any in the literature.

If I am wrong and the literature does indeed contain unification efforts from a left-right point of view, please give the references in the answer!

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A gauge group of only G^L x G^R, with left-handed fermions coupling to G^L and right-handed fermions coupling to G^R, means that there aren't any gauge bosons that couple to left and to right. Whereas in the standard model, it's e.g. the same SU(3) gluons which couple to left and to right.

There is some work on GxG, e.g. Ernest Ma on SO(10)xSO(10), but it would be about breaking to the diagonal subgroup.

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  • $\begingroup$ You could get extra gauge groups from Kaluza-Klein! $\endgroup$ – Mitchell Porter Jul 28 '17 at 1:25
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    $\begingroup$ How do you know it's the "same" SU(3) gluons? $\endgroup$ – zooby Jul 2 '18 at 19:58
  • $\begingroup$ Weird idea! The strong gauge group would be SU(3)L x SU(3)R, with chiral quarks also still interacting via Higgs yukawa terms. $\endgroup$ – Mitchell Porter Jul 2 '18 at 20:24
  • $\begingroup$ There are already models where color SU(3) is actually the diagonal subgroup of two separately gauged SU(3)s, but I never saw this chiral segregation before. $\endgroup$ – Mitchell Porter Jul 2 '18 at 23:39

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