On infinite symmetry algebras in Yang-Mills theory

• Published in: The journal of high energy physics Vol. 2023; no. 12; pp. 9 - 45
• Main Authors: Freidel, Laurent, Pranzetti, Daniele, Raclariu, Ana-Maria
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2023; Springer Nature B.V; SpringerOpen
• Subjects: Algebra; Classical and Quantum Gravitation; Closed loops; Commutators; Conformal and W Symmetry; Elementary Particles; Gravity; High energy physics; Higher Spin Symmetry; Mathematical analysis; Operators (mathematics); Physics; Physics and Astronomy; Polynomials; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Space-Time Symmetries; String Theory; Symmetry; Yang-Mills theory; Space-Time Symmetries; Conformal and W Symmetry; Higher Spin Symmetry
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP12(2023)009

A bstract 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+∞ .