Nonperturbative double copy: worldline instantons, color thermality, and backreaction

TL;DR

This work develops a non-perturbative worldline instanton framework for vacuum decay in the Yang-Mills root of a Schwarzschild background and shows that color thermality arises from a topological winding, with a universal color temperature $T_c \\propto 1/(g Q)$. By abelianizing the YM root in a Kerr-Schild background, the authors map the gauge-theory vacuum response to a gravitational dual via the double copy, and they demonstrate that color charge conservation induces a quadratic backreaction in the decay exponent, mirroring the Parikh–Wilczek correction in gravity. The non-abelian root thus exhibits universal thermality and non-linear backreaction that survive the double-copy mapping, whereas the Abelian shadow fails to reproduce these features. Collectively, the results bolster the non-perturbative validity of the double copy and illuminate how horizon thermodynamics may be encoded in the kinematic/algebraic structure of gauge theories, with potential implications for macroscopic color states and quantum-information scenarios.

Abstract

We present a first-principles, non-perturbative worldline instanton analysis of vacuum decay in the non-abelian Yang-Mills root of a Schwarzschild background. We recover the gauge theory color-thermal spectrum as a topological winding mode. The double copy maps vacuum response from the gauge theory directly to the gravity theory. Furthermore, the decay exponent acquires a universal quadratic correction from color charge conservation, showing that the double copy correctly captures the non-linear backreaction as required for unitarity.