Spontaneous symmetry lowering of the SO(N,3N) metric field interacting with the massles spinor

The symmetry broken solution (ground state) of the $SO(N,3N)$field theory is calculated by nonperturbative methods ($N$-times repeated Hubbard–Stratonovich transformation).The high symmetry fields are $4N$ dimensional metrics tensor and $2^{2N}$ dimensional spinor. The low symmetry fields are sum of $4$ dimensional metrics tensors and product of $4$ dimensional  super–symmetric spinors of the $SO(1,3)$. All the efforts are made to find the solution where each embedded $SO(1,3)$ subspace get its own scale (shrink or expansion) breaking the global $SO(N,3N)$ symmetry.

This work is not finished; publishing the most of what I was able to do


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