Covariant Phase Space and Soft Factorization in Non-Abelian Gauge Theories
Temple He, Prahar Mitra
TL;DR
The paper uses the covariant phase space formalism to analyze the infrared structure of massless non-Abelian gauge theories, revealing an infinite vacuum degeneracy sourced by boundary gauge data at null infinity. By constructing a phase-space factorization into soft and hard gauge sectors and quantizing it, the authors derive a Ward identity that relates amplitudes between arbitrary in/out vacua to standard perturbative QFT amplitudes, enabling explicit S-matrix factorization across vacua. They show that the leading single and multiple soft gluon theorems emerge as consequences of this Ward identity, providing a unifying framework for soft factorization in non-Abelian gauge theories and clarifying the role of infinite vacuum degeneracy in infrared behavior. The results have implications for understanding infrared divergences, asymptotic symmetries, and the holographic-like structure of gauge theories at null infinity.
Abstract
We perform a careful study of the infrared sector of massless non-abelian gauge theories in four-dimensional Minkowski spacetime using the covariant phase space formalism, taking into account the boundary contributions arising from the gauge sector of the theory. Upon quantization, we show that the boundary contributions lead to an infinite degeneracy of the vacua. The Hilbert space of the vacuum sector is not only shown to be remarkably simple, but also universal. We derive a Ward identity that relates the n-point amplitude between two generic in- and out-vacuum states to the one computed in standard QFT. In addition, we demonstrate that the familiar single soft gluon theorem and multiple consecutive soft gluon theorem are consequences of the Ward identity.