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Peer review Supersymmetry from the Universal Equation - Dynamical Breaking, Generalized Index, and Spectral Predictions Witten

Livolsi, Edoardo
PhilArchive · Papers
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philosophy
Supersymmetry has long been regarded as a mathematically elegant extension of quantum field theory, yet its physical realization remains uncertain: the scale of supersymmetry breaking is undetermined, the superpartner spectrum is unconstrained, and the Witten index provides only a topological counting principle without dynamical restriction. This paper shows that a closed global spinorial variational functional generates supersymmetric structures as emergent consequences of an admissibility condition on relational spinor configurations. The supersymmetry algebra arises from the fluctuation structure around admissible configurations, rather than being postulated as a fundamental symmetry. Within this framework the supersymmetry breaking scale is not introduced arbitrarily but follows from the internal balance of the functional terms, producing a dynamically determined energy scale. The construction also leads to a generalized form of the Witten index in which the trace is restricted by a global normalization constraint on the spinorial field. This modification removes the large degeneracies typical of conventional supersymmetric models and selects a discrete set of admissible states. The surviving configurations exhibit a golden-structured spectral organization, providing a falsifiable prediction for possible remnants of supersymmetric sectors. Supersymmetry therefore appears not as a fundamental principle but as a derived structure emerging from a deeper global consistency condition on spinorial fields. The framework replaces phenomenological arbitrariness with structural necessity and converts several open issues of supersymmetric theories into consequences of a single admissibility principle.
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