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Stephen Adler's SU(8) theory of everything

  1. Mar 17, 2014 #1
    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)/Z5, 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.
    Last edited: Mar 17, 2014
  2. jcsd
  3. Mar 17, 2014 #2


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    Dearly Missed

    Last edited: Mar 17, 2014
  4. Mar 17, 2014 #3


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    Adler, with Bell and Jackiw, is a co-discoverer of the axial anomaly.
  5. Mar 20, 2014 #4


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    Indeed. And still, a bit of outsider, because of the quaternionic thing. I like the mix.
  6. Mar 20, 2014 #5


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    He was also a pioneer in the current algebras before the standard model came to be, especially the Adler sum rules. Incredibly prolific: well over 100 serious papers in arxiv since 1994, which represents substantially less than half his career! (I've been a 'fan' for a long time).

    A summary of his work:

  7. Mar 23, 2014 #6


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    Could Adler's paper renew interest in E(8) unification? Something like E(8) > E(7) x SU(2) > SU(8) x SU(2). Could Adler's particle content and LQG together fit into E(8)? Crazy thoughts. Surely, the weak limit linear gravity is a weak point of his scheme. In the paper he suggests that searching for a bigger group is his next step.... Hopefully Jacques Distler steps in to fill in the details :)


    NB I do not think that Adler sees his paper as a ToE. The title of this thread could better use the phrase Unification in the sense as for EW unification, a step but not the last.
    Last edited: Mar 23, 2014
  8. Mar 31, 2014 #7
    I used my Lie-algebra code on this proposed GUT model, and I found:

    SU(8) -> SU(5)*SU(3)*U(1)

    63 = (24,1,0) + (1,8,0) + (0,0,0) + (5,3*,1) + (5*,3,-1)
    Antisymmetric tensors:
    1 = (1,1,0)
    8 = (5,1,3/8) + (1,3,-5/8)
    28 = (5,3,-1/4) + (10,1,3/4) + (1,3*,-5/4)
    56 = (5,3*,-7/8) + (10,3,1/8) + (10*,1,9/8) + (1,1,-15/8)
    70 = (5,1,-3/2) + (10,3*,-1/2) + (10*,3,1/2) + (5*,1,3/2)
    56* = (10,1,-9/8) + (10*,3*,-1/8) + (5*,3,7/8) + (1,1,15/8)
    28* = (10*,1,-3/4) + (5*,3*,1/4) + (1,3,5/4)
    8* = (5*,1,-3/8) + (1,3*,5/8)
    1' = (1,1,0)

    Let's see what can give the Georgi-Glashow model:
    SU(5) -> SU(3)*SU(2)*U(1)

    SU(5) mass terms (left-handed):
    Up: F(10).F(10).H(5)
    Neutrino: F(5*).F(1).H(5)
    Down, electron: F(10).F(5*).H(5*)
    MSSM Higgs mu: H(5).H(5*)
    RH nu Maj mass: F(1).F(1)

    F = elementary fermion (3 generations), H = Higgs particle (1 generation? 3 generations?)

    I find lots of possibilities for some of those mass terms.
  9. Mar 31, 2014 #8
    At first sight, these antisymmetric-tensor irreps suggest this superalgebra: SO(16)

    SO(16) -> SU(8) * U(1)

    This connects to E8:
    E8 -> SO(16)
    248 -> 120 (adjoint) + 128 (one of the two spinors, which are each self-dual)

    A problem with SO(16) -> SU(8), however:
    One spinor -> 1 + 28 + 70 + 28* + 1'
    The other spinor -> 8 + 56 + 56* + 8*

    So it does not fit as well with chirality, because all these irreps share chirality. One doesn't have an important feature of the Standard Model, SU(5), SO(10), and E6, where one gets EF rep duality fitting in with EF reversed chirality.

    Let's try E8 -> E7 * SU(2)
    248 -> (133,1) + (1,3) + (56,2)
    Adjoint, scalar, fundamental

    Now E7 -> SU(8)
    56 -> 28 + 28*
    AS 2-tensor and its dual
    133 -> 63 + 70
    Adjoint, AS 4-tensor
  10. Mar 31, 2014 #9
    I tried finding SU(8) versions of the SU(5) mass terms, but I could not get sensible results.

    Adler's field content:

    Graviton: spin = 2, rep = 1 (scalar), hel = 2
    Vector-spinor: spin = Weyl 3/2, rep = 8 (vector) for L, hel = 16
    Vector: spin = 1, rep 63 (adjoint), hel = 126
    Spinor: spin = Weyl 1/2, rep = 56 (AS 3-tensor) for L, hel = 112
    Boson, fermion hel = 128

    Spinor (two of them): spin = Weyl 1/2, rep = 28* (dual AS 2-tensor) for L, hel = 112
    Scalar (complex): spin = 0, rep = 56 (AS 3-tensor), hel = 112
    Boson, fermion hel = 112

    hel = number of helicity states, rep = representation, L = left-handed chirality

    There aren't any sensible interaction terms with 2 or 3 spinor particles. For 4 of them, they'd all have rep 28*. A rep 56 is equivalent to two rep 28* particles here, so for 5 particles, 3 would be 28*'s, and 2 would be 56's.

    So to get to a more typical GUT like Georgi-Glashow or flipped SU(5), one would need some complicated symmetry breaking. It would need to produce the mass matrices, which completely break the SU(3) generation symmetry of this model.
  11. Jul 3, 2014 #10


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    New version of Adlers paper appeared. Happy to see his added hint about E(8). A faint proof that he actually reads this forum :)

  12. Jul 6, 2014 #11


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    If it's not supersymmetric, then what's the motivation for including a gravitino? Isn't that just hypothesized as the supersymmetric partner of the graviton?
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