Bottom-up open EFT for non-Abelian gauge theory with dynamical color environment

TL;DR

This paper introduces a local open effective field theory for non-Abelian gauge theories that explicitly includes environmental variables, capturing dissipation, memory effects, and color transport in non-Abelian plasmas.

Contribution

It develops a gauge-covariant, local open EFT framework with dynamical environment variables for non-Abelian gauge theories, extending the understanding of dissipative color dynamics.

Findings

Natural emergence of hard thermal loop response as environmental response

Framework captures nonlocal dissipation and stochastic effects systematically

Provides a basis for dissipative Yang--Mills effective field theories

Abstract

We develop a bottom-up open effective field theory (EFT) for non-Abelian gauge theories within the Schwinger--Keldysh formalism. Instead of integrating out the environment completely and starting from a nonlocal influence functional, we retain the slow environmental response variables explicitly and construct a local system-environment EFT. The environmental sector is described by a dynamical color-frame variable, St\"uckelberg-like field, and an associated color-current sector, which gives the nontrivial interactions and dissipation between the system and the environment. The resulting construction provides a gauge-covariant Markov embedding of nonlocal and non-Markovian color response. After integrating out the retained environmental variables with retarded boundary conditions, the reduced system theory acquires nonlocal dissipative kernels and stochastic sources. We show that the hard thermal loop response arises naturally as a particular realization of the retained environmental response. Our framework provides a local open-EFT description of color transport, memory effects, and fluctuation-dissipation structure in non-Abelian plasmas, and offers a systematic starting point for dissipative Yang--Mills EFTs with dynamical environments.