The main result is a reported threshold in loop size. In an arXiv preprint, a calculated Yang-Mills channel grows for smaller loops and decays for larger ones when an exploratory loop-size infrared regulator is imposed. At lambda = 0.1, the crossing is at a critical diameter of about 1.8 when measured in Debye units. The calculation concerns pure SU(N) Yang-Mills at large N, weak 't Hooft coupling and 3+1 dimensions. The numerical exponent comes from class (ii) only. The leading-in-colour class (i) channel remains unsolved, so this is not the full leading-large-N result.
The change is described as continuous, rather than as a jump between two fixed states. The exponent crosses zero at a critical radius, R*, and the reported scrambling time diverges at that point. In this model, smaller loops have a finite scrambling time, while larger loops do not scramble. These statements apply to the regulated class-(ii) calculation.
A calculation of one channel
To build the possible growth channels, the analysis pairs eight fields at leading order. It considers 105 pairings. Of those, 69 cancel, leaving 36 surviving contractions arranged in three topologies. Those topologies define the candidate ladder channels used in the calculation.
For class (ii), the problem is written as a Bethe-Salpeter eigenvalue equation, where the relevant eigenvalue signals growth or decay. Numerically, the calculation diagonalizes a 48-dimensional matrix on a geometric rail-momentum grid running from 0.5T to 4T. The threshold is located by interpolating the last change from growth to decay.
The infrared problem
The key uncertainty is the infrared part, the low-scale end of the calculation. Without an imposed infrared cutoff, the exponent remains sensitive to the magnetic scale through the rail-width logarithm and soft-rung integrals. The paper says the exponent cannot be computed within this treatment unless a decay-width calculation retains that infrared sensitivity.
The preprint uses an exploratory loop-size regulator for this part of the calculation. The prescription treats exchanges below a loop-size-dependent cutoff as invisible and replaces the infrared end of the damping logarithm with 1/(2R). It is a hard loop-size prescription, and the computation does not supply a first-principles smooth damping treatment.
Within that prescription, lambda = 0.1 gives the reported growth-to-decay crossing near 1.8 Debye units. Across the fitted range from 0.005 to 0.15 in lambda, the critical diameter and radius follow the paper's reported coupling-dependent fits. The fit is described as numerically consistent with a magnetic infrared length, but the paper says further work is needed to establish whether the threshold is physical beyond the imposed prescription.
A conjecture beyond the numerics
Alongside the numerical work, the operator-evolution analysis finds operator growth only when the gauge group is non-abelian and the number of spacetime dimensions is greater than two. The authors extend that finding into a broader conjecture: pure-gauge theories are chaotic only in that regime. The paper presents this as a conjecture, not as a completed proof of a general chaos criterion.
The paper also reports stronger large-N suppression for the loop's out-of-time-order correlator, or OTOC, than for the generic counting quoted for single-trace operators. That scaling comparison does not determine the full leading-large-N exponent. The relative growth rates of the unresolved channels are still unknown, and class (i) remains unsolved.
What is still missing
The numerical result therefore has a narrow scope. It does not include a first-principles smooth treatment of damping, the leading-in-colour class-(i) ladder, or nonzero injected momentum. It also does not calculate the corresponding butterfly velocity. Those omissions leave the reported exponent as a class-(ii) result under the cutoff prescription, rather than a complete leading-large-N answer.
The strong-coupling discussion is also a proposal, not a result. It outlines a cobordism and string-based framework that would require a four-string amplitude in a confining background, but the preprint does not provide a controlled amplitude.
Further progress would have to address the infrared decay width and the unsolved class-(i) ladder, as well as finite-momentum behavior and the missing butterfly-velocity calculation. The proposed strong-coupling route would still need its controlled four-string amplitude. The document is an arXiv preprint, version 1, dated 25 Aug 2026.
Paper data and sources
Original title: Chaos in Yang-Mills
Authors: Barel Skuratovsky
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-25
DOI: Not available
Original paper · Full text