On infinite symmetry algebras in Yang-Mills theory

TL;DR

This paper constructs and proves the closure of an infinite-dimensional loop algebra of higher-spin symmetries in Yang-Mills theory, revealing how these symmetries constrain the theory's nonlinear structure.

Contribution

It explicitly constructs higher-spin charge aspects in Yang-Mills theory as polynomial operators and proves their algebraic closure to quadratic order, demonstrating the symmetry's role.

Findings

Higher-spin charges form a closed loop algebra in Yang-Mills

The algebra constrains the nonlinear structure of the theory

Similar algebraic structures are shown in gravity for quadratic charges

Abstract

Similar to gravity, an infinite tower of symmetries generated by higher-spin charges has been identified in Yang-Mills theory by studying collinear limits or celestial operator products of gluons. This work aims to recover this loop symmetry in terms of charge aspects constructed on the gluonic Fock space. We propose an explicit construction for these higher spin charge aspects as operators which are polynomial in the gluonic annihilation and creation operators. The core of the paper consists of a proof that the charges we propose form a closed loop algebra to quadratic order. This closure involves using the commutator of the cubic order expansion of the charges with the linear (soft) charge. Quite remarkably, this shows that this infinite-dimensional symmetry constrains the non-linear structure of Yang-Mills theory. We provide a similar all spin proof in gravity for the so-called global quadratic (hard) charges which form the loop wedge subalgebra of $w_{1+\infty}$.