Infinite-dimensional hierarchy of recursive extensions for all sub$^n$-leading soft effects in Yang-Mills

TL;DR

This paper develops a comprehensive framework for understanding all orders of sub$^n$-leading soft effects in Yang-Mills theory by constructing an extended phase space and recursive charge relations, applicable at tree and loop levels.

Contribution

It introduces a hierarchical, recursive construction of charges for all sub$^n$-leading soft effects in Yang-Mills, unifying their algebraic structure and extending previous approaches.

Findings

Constructed extended phase space including asymptotic symmetries and charges.

Derived recursive relations for sub$^n$-leading charges at all orders.

Connected the algebraic structure to infinite-dimensional algebras in conformal field theory.

Abstract

Building on our proposal in arXiv:2405.06629, we present in detail the construction of the extended phase space for Yang-Mills at null infinity, containing the asymptotic symmetries and the charges responsible for sub$^n$-leading soft theorems at all orders. The generality of the procedure allows it to be directly applied to the computation of both tree and loop-level soft limits. We also give a detailed study of Yang-Mills equations under the radial expansion, giving a thorough construction of the radiative phase space for decays compatible with tree-level amplitudes for both light-cone and radial gauges. This gives rise to useful recursion relations at all orders between the field strength and the vector gauge coefficients. We construct the sub$^n$-leading charges recursively, and show a hierarchical truncation such that each charge subalgebra is closed, and their action in the extended phase space is canonical. We relate these results with the infinite-dimensional algebras that have been recently introduced in the context of conformal field theories at null infinity. We also apply our method to the computation of non-universal terms in the sub-leading charges arising in theories with higher derivative interaction terms.