Chaos in Yang-Mills

Abstract

We study the dynamics of pure-gauge SU(N) through the time evolution of a spatial Wilson loop. We compute its out-of-time-order correlator at weak 't Hooft coupling and large N, and propose a framework for the strong-coupling description. We find that operators in pure-gauge Yang-Mills grow only when the group is non-abelian and d>2, and conjecture that pure gauge theories are chaotic only when non-abelian at d>2. Even at weak coupling the correlator's exponent inherits the IR sensitivity of the gluon self-energy imaginary part, which rests on the non-perturbative magnetic scale. We then explore the possibility that the loop's own size supplies that scale, since the loop operator is blind to any momenta softer than 1/2R. With the cutoff imposed that way the exponent changes sign at a critical diameter: smaller loops scramble, larger ones do not, and the scrambling time diverges at the crossing. The transition follows from that cutoff. Further investigation, in particular a first-principles treatment of the thermal decay width, is required to establish whether it is physical.