Supersymmetric SO(N) from a Planck-scale statistical theory

TL;DR

This paper refines a theoretical framework starting from a Planck-scale statistical model, leading to supersymmetry and SO(N) gauge interactions, with improved treatments of path integrals, supersymmetry, and invariance transformations.

Contribution

It provides new, more satisfactory methods for transforming the path integral and supersymmetry from initial Euclidean forms to standard Lorentzian and supersymmetric forms.

Findings

Enhanced transformation techniques for fermionic and bosonic path integrals.

Refined derivation of supersymmetry from a primitive statistical model.

Achieved invariance of the action under general coordinate transformations.

Abstract

Several refinements are made in a theory which starts with a Planck-scale statistical picture and ends with supersymmetry and a coupling of fundamental fermions and bosons to SO(N) gauge fields. In particular, more satisfactory treatments are given for (1) the transformation from the initial Euclidean form of the path integral for fermionic fields to the usual Lorentzian form, (2) the corresponding transformation for bosonic fields (which is much less straightforward), (3) the transformation from an initial primitive supersymmetry to the final standard form (containing, e.g., scalar sfermions and their auxiliary fields), (4) the initial statistical picture, and (5) the transformation to an action which is invariant under general coordinate transformations.