The Black Death Anomaly: A Non-Abelian Field Theory of Epidemiological Safe Zones

TL;DR

This paper introduces a non-Abelian gauge theory framework to explain the formation of safe zones during the Black Death, revealing that these zones are topologically necessary features of pathogen dynamics rather than anomalies or quarantine effects.

Contribution

It develops a novel non-Abelian field theory model for epidemic spread, linking spatial mutation waves to topological safe zones, and analytically explains historical safe zones as topological features.

Findings

Safe zones emerge as topological voids in the model.

Traveling mutation waves are driven by covariant advection.

The model predicts stable, isotropic survival regions matching historical data.

Abstract

Classical reaction-diffusion models of the 14th-century Black Death fail to explain the rapid genetic radiation of \textit{Yersinia pestis} and the anomalous emergence of vast, untouched geographic safe zones, such as Central Europe. In this work, we resolve these historical anomalies by embedding macroscopic pathogen dynamics within a non-Abelian gauge theory. Utilizing the Doi-Peliti formalism, we map the stochastic master equation of a multi-strain epidemic into a covariant classical field theory. We introduce an $SU(N)$ environmental gauge field, $\mathbf{A}_\mu$, which actively couples geographic displacement to phenotypic mutation, treating evolutionary drift as a spatial transport phenomenon. We demonstrate via linear stability analysis that this covariant advection drives a Differential Flow (Turing-Hopf) instability, spontaneously breaking spatial symmetry to generate traveling waves of mutation. Furthermore, by extending the pathogen multiplet to the large-$N$ ('t Hooft) continuum limit, we prove that historical safe zones are not statistical outliers nor the result of perfect quarantine, but are mathematically necessary topological voids. In this continuous limit, the destructive interference of the mutating wavefronts analytically resolves into a stable, isotropic macroscopic node governed by a zeroth-order Bessel function ($J_0$), precisely mapping onto the historical survival of Poland and Bohemia.