A Ward-Balanced Δ–Σ Fixed Point and the Emergence of a Light Cone and the Arrow of Time

Abstract

We present a minimal pre-geometric framework built from two opposing vacuum sectors, Δ (contractive) and Σ (expansive). Ward consistency constrains the renormalization-group flow of their ratio α ≡ Δ/Σ, while structural stability selects the non-trivial infrared-stable fixed point α* = 3/2 within the minimal Ward-balanced framework developed in this work. This value is not introduced phenomenologically but emerges from the combined Ward-constrained RG structure and structural-stability analysis. A concrete microscopic realization compatible with the effective Ward-balanced framework is presented in the Supplementary Information. The central results derived in this work are independent of the particular microscopic realization and depend on the universal Ward-balanced infrared fixed-point structure. At this fixed point the framework yields an emergent invariant light cone (Z_t = Z_x) and an emergent Lorentzian causal structure without assuming a prior spacetime geometry. The same Ward-protected projection from the pre-geometric sector to emergent spacetime naturally gives rise to an intrinsic arrow of time through reduced GKSL dynamics, thereby providing a common pre-geometric origin for both causal structure and temporal irreversibility. The construction is formulated entirely within standard field-theoretic tools. Beyond establishing a common pre-geometric origin for the emergent light cone and the arrow of time, it predicts a concrete and experimentally testable phenomenological signature: a correlated two-scale Δ-sector structure consisting of a Δ–Higgs admixture near 125 GeV together with a heavier Δ-dominated scalar companion at TeV energies. Full technical derivations and microscopic realizations are provided in the Supplementary Information.