13/15. The weakness of string theory revisited


Superman + kryptonite (1978)


LHC − superpartners (2017)

Standard arguments for supersymmetry (super = fermionic):

  1. Nature has fermions.
    Polchinski (1995) taught us that fermions can live on D-branes.
  2. Evades Coleman-Mandula (1967) no-go theorem.
    Spin(11,1) obeys theorem: Dirac and internal algebras always commute.
  3. Gets 3 coupling parameters of standard model to meet at grand unification.
    Spin(11,1): 3 couplings meet in 2 separate steps.
  4. The ground state of bosonic strings is tachyonic, therefore unstable.
    In cosmology, high energy vacua are unstable by the Higgs mechanism. Are these the tachyons?
  5. Fermion-boson infinities cancel each other in scalar boson masses.
    Can standard particle qft be applied to the electroweak Higgs boson?
  6. Magically cancels gauge anomalies in string theory.
    Spin(11,1): gauge anomalies vanish because the theory is chirally balanced.

Problems with supersymmetry:

  1. Predicts symmetries that are not observed.
    Spin(11,1) is not supersymmetric.
  2. Preempts symmetries that are observed.
    Spin(11,1) possesses the symmetries that are observed.

Supersymmetry algebra posits that anticommutators of \(R,L\)-handed spinor generators \(Q\) generate translations \(P\): \[ \{ Q_R , Q_L \} = P \ , \quad [ P , P ] = 0 \ . \] But Brauer-Weyl (1935) theorem shows \[ \bigl[ \{ Q_R , Q_L \} , \{ Q_R , Q_L \} \bigr] = \{ Q_R , Q_R \} + \{ Q_L , Q_L \} \ , \] which are the observed symmetries of the standard model.

 -> 14/15. The multiverse just got a whole lot bigger
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