A structural criterion for asymptotic states in Supersymmetry

TL;DR

The paper investigates whether algebraically present fields in supersymmetric theories necessarily admit localized asymptotic particle states. It introduces a minimal, predynamical localization criterion based on long-time stability against slow environmental fluctuations represented by an effective background $\\Xi(x)$, without altering the underlying dynamics. It shows a qualitative dichotomy: fermionic modes can retain phase coherence and satisfy localization, while scalar modes generically decohere due to stochastic mass modulation, precluding a real mass pole in the LSZ sense. This provides a conservative, model-independent explanation for how supersymmetry’s algebraic structure can coexist with an asymmetric observable spectrum, with localization as an independent structural requirement and broad implications for SUSY and supergravity contexts.

Abstract

In quantum field theory, the algebraic existence of a field does not guarantee the existence of a corresponding localized asymptotic particle state. This distinction is well established in the presence of infrared effects, long-range correlations, and environmental interactions, and becomes particularly relevant in supersymmetric theories, where fermionic and bosonic degrees of freedom are constrained at the algebraic level but need not share identical asymptotic behavior. In this work we introduce a minimal and predynamical localization criterion that distinguishes algebraically allowed degrees of freedom from those capable of forming stable, phasecoherent asymptotic states. The criterion is formulated in terms of long-time stability under slow structural fluctuations of an effective background, without modifying the underlying field equations or introducing new physical interactions. We show that fermionic and scalar fields respond qualitatively differently to such structural effects. While fermionic modes may retain asymptotic stability, scalar modes generically exhibit decoherence and damping, preventing their interpretation as localized one-particle states. This provides a conservative and model-independent perspective on how supersymmetric algebraic structures may coexist with an asymmetric observable particle spectrum. The analysis is intentionally non-constructive and does not rely on specific supersymmetrybreaking mechanisms, cosmological assumptions, or new dynamical ingredients. Rather, it clarifies localization as an independent structural requirement for particle existence within standard quantum field theory.