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SU(8) unification with boson-fermion balance

Stephen L. Adler

(Submitted on 9 Mar 2014)

We formulate an SU(8) unification model motivated by requiring that the theory should incorporate the graviton, gravitinos, and the fermions and gauge fields of the standard model, with boson--fermion balance. Gauge field SU(8) anomalies cancel between the gravitinos and spin 1/2 fermions. The 56 of scalars breaks SU(8) to SU(3)_{family}×SU(5)/Z_{5}, with the fermion representation content needed for ``flipped'' SU(5), and with the residual scalars in the representations needed for further gauge symmetry breaking to the standard model. Yukawa couplings of the 56 scalars to the fermions are forbidden by chiral and gauge symmetries. In the limit of vanishing gauge coupling, there are N=1 and N=8 supersymmetries relating the scalars to the fermions, which restrict the form of scalar self-couplings and should improve the convergence of perturbation theory, if not making the theory finite and ``calculable''. In an Appendix we give an analysis of symmetry breaking by a Higgs component, such as the (1,1)(−15) of the SU(8) 56 under SU(8)⊃SU(3)×SU(5)×U(1), which has nonzero U(1) generator.

This is an odd but interesting paper - an attempt to describe a field-based theory-of-everything that resembles N=8 supergravity but which isn't actually supersymmetric. As in supersymmetry, the number of bosonic and fermionic degrees of freedom is the same, and the nongravitational part of the theory has some supersymmetries in the limit of zero coupling.

Back before the 1984 superstring revolution, when supergravity was the hottest unification theory available, there were some attempts to find the standard model inside N=8 supergravity that were ingenious but strained. This theory of Adler's comes from the other direction - he takes a common GUT framework (plus gravitinos) and then bends it to look like an N=8 supermultiplet. Those of us who have attempted something similar, should see if Adler is onto something.

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# Stephen Adler's SU(8) theory of everything

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