History-Dependent Gravity XXVII: Dynamical Chiral Symmetry Breaking from Temporal Memory

This paper (Paper XXVII of the History-Dependent Gravity series) extends the HDG framework to the fermionic sector of Quantum Chromodynamics (QCD), demonstrating that dynamical chiral symmetry breaking (DCSB) and its thermal restoration emerge naturally from temporal memory effects. By introducing a gauge-invariant nonlocal fermionic kernel, we derive the functional renormalization group (FRG) flow of four-fermion interactions induced by the memory kernel. We show that the infrared enhancement of the memory kernel destabilizes the chirally symmetric fixed point, generating a constituent quark mass M(0)≈268M(0)≈268 MeV without phenomenological fine-tuning. Furthermore, solving the finite-temperature gap equation reveals that the chiral crossover temperature is dynamically controlled by the memory anomalous dimension ηKηK. While a local kernel (ηK=0ηK=0) predicts an unphysical condensate melting temperature (∼65∼65 MeV), the physical effective-model scale (Tpeak≈221Tpeak≈221 MeV) is uniquely recovered for ηK≈0.4ηK≈0.4. Crucially, all observables are obtained from a single memory kernel without retuning parameters between zero and finite temperature. This establishes temporal nonlocality not merely as a correction, but as a fundamental structural ingredient governing infrared binding and QCD vacuum stability. The work provides a unified, non-Markovian alternative to local effective models (e.g., NJL), with direct implications for lattice QCD comparisons and future meson spectroscopy.