2025/06/18 by Ferreira, L. A., Malavazzi, H. · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Chromodynamics and Particle Interactions #Quantum and Classical Electrodynamics
paper · pdf · doi:10.48550/arxiv.2506.15832
openalex publication_date 2025/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that classical, non-supersymmetric Yang-Mills theories coupled to spin-1/2 and spin-0 elementary matter fields, in (3+1)-dimensional Minkowski space-time, possess exact structures that resemble integrability, with an infinite number of conserved charges in involution. Such structures live in the space of non-abelian electric and magnetic charges, and are based on flat connections in generalized loop spaces, presenting an R-matrix, and Sklyanin relation. We present two novel symmetries of Yang-Mills theories. The first one corresponds to global transformations generated by the infinity of those conserved charges under the Poisson brackets. The gauge and matter fields, as well as Wilson lines and fluxes, have interesting transformation laws under such a global symmetry. The second one corresponds to symmetries of the integral Yang-Mills equations, which lead to the conserved charges. They generate an infinite-dimensional group, where the elements are holonomies of connections on the loop space of functions from the circle S1 to the space-time. Our approach certainly applies to the Standard Model of the Fundamental Interactions. The conserved charges are gauge invariant, and so, in the case of QCD, they are color singlets and perhaps are not confined. Therefore, the hadrons may carry such charges. Our results open up the way for the construction of non-perturbative methods for Yang-Mills theories.