SUSY has been also a problem of TGD for decades. TGD forces a huge extension of super-conformal invariance by replacing 2-D surfaces with 3-D light-like surfaces. The extended super-conformal and super-symplectic symmetries characterize also the light-cone boundary of 4-D Minkowski space with points replaced with CP2 making the dimension of M4 unique. M4×CP2 is also forced by the existence of twistor lift of TGD.
TGD SUSY must conserve fermion number. How? TGD allows separate conservation of baryon and lepton number and the idea was that right-handed neutrino generates the least broken SUSY as N=2 supersymmetry. The idea was wrong.
The generalization of super-space geometry to a super-geometry of sub-manifolds led to a beatiful generalization of super-imbedding space in which coordinates are hermitian and their superparts are sums of monomials of quarks and antiquarks with vanishing quark number. Leptons are also possible but they are not necessary and actually excluded by SO(1,7) triality.
This also led to a generalization of second quantization of quark field implying SUSY as side product: in particular, theta parameters are replaced with oscillator operators for sparticles are created by local composites of quark oscillator operators. This is something totally new. Number theoretical vision plays crucial role in the picture.
Quark super spinors can have similar structure and the monomials in their expansion possess same electroweak quantum numbers as quarks. Leptons can be regarded as local composites of 3 antiquarks and thus spartners of quarks. SUSY would have been staring us directly to eyes for almost a century! Matter antimatter asymmetry is generated because small CP breaking predicted by TGD favors local composites of quarks as leptons over non-local composites for antibaryons. Standard model spectrum is predicted apart from pseudoscalar for which there exist indications from LHC at correct mass.
The outcome is an explicit proposal for S-matrix: S-matrix would be given by super-variant of the exponential of action defining the super-Kaehler function of "world of classical worlds" (WCW) generalized to super-Kaehler geometry. The construction of unitary S-matrix has been second challenge of TGD for decades. Rather precisely 41 years after the emergence of the basic idea of TGD I can say that it is done now!
Against this background it is somewhat frustrating to see colleagues busily planning new super-collider to test a wrong vision about SUSY already known to be excluded by LHC findings.
For details see the article Recent view about SUSY in TGD Universe .
For a summary of earlier postings see Latest progress in TGD.