Year: 2026
Type: article
Abstract: We construct and classify exact complex plane-wave solutions of the vacuum SU(2) Yang–Mills equations using a simple ansatz for the gauge potentials. By reducing the nonlinear Yang–Mills equations to algebraic constraint conditions, we obtain a complete classification. For nonzero coupling and nonvanishing transverse and color-space parameters, the solutions can be reduced to a single fixed color generator by an SU(2) gauge transformation if and only if → 𝛽 × → ℓ = 0 . Therefore, the genuinely non-Abelian solutions are precisely those with → 𝛽 × → ℓ ≠ 0 , occurring in subbranches of Cases (iii) and (vi). Their field strengths are of plane-wave type, satisfy the standard dispersion relation 𝜔 = 𝑐 𝑘 , and contain a nonlinear second harmonic proportional to ( → 𝛽 × → ℓ ) · → 𝑆 . Although their quadratic Lorentz invariants vanish, the gauge-invariant Hermitian energy density can remain nonzero and exhibit a bounded modulation. We also show that a common amplitude rescaling generates an exact zero-action critical family connecting the vacuum to genuinely non-Abelian waves, with the phase-averaged Hermitian energy density growing nonlinearly with the amplitude. We further extend the solutions to arbitrary smooth wave profiles and construct a complex external current that generates a non-Abelian pulse from vacuum. Using this pulse as a background, we obtain an explicit relation between a probe gluon’s incoming and outgoing color amplitudes. These results provide a complete and transparent classification of Abelian-type and genuinely non-Abelian propagating waves in SU(2) Yang–Mills theory.
Source: Nuclear Physics B
Authors: Yu-Xuan Zhang, Jing-Ling Chen
Institution: Nankai University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Awards: G3713333881, G4427997861
OpenAlex ID: W7224124121