Condensation and prescaling in spatial Polyakov loop correlations far from equilibrium

The far-from-equilibrium dynamics of spatial Polyakov loop correlations, which provide gauge-invariant observables akin to effective particle numbers for gluon plasmas, are investigated within real-time <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>SU</a:mi><a:mo stretchy="false">(</a:mo><a:msub><a:mi>N</a:mi><a:mi>c</a:mi></a:msub><a:mo stretchy="false">)</a:mo></a:math> lattice gauge theory at weak couplings and large gluon occupations. The momentum zero mode of these correlations reveals the dynamic formation of a condensate, while at nonzero momenta, energy is transported toward the ultraviolet. We demonstrate that the nonzero momentum dynamics is well described by a direct cascade in terms of gauge-invariant Polyakov loop excitations, exhibiting self-similar prescaling indicative of a nonthermal attractor. This behavior can be analytically understood through perturbation theory for the Polyakov loop correlations and the established dynamics of gauge field correlations. We perform simulations for both SU(2) and SU(3) gauge groups, providing further consistency checks on the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:msub><e:mrow><e:mi>N</e:mi></e:mrow><e:mrow><e:mi>c</e:mi></e:mrow></e:msub></e:mrow></e:math> dependence of perturbative expectations. No evidence of an inverse cascade toward lower momenta is found for momenta above the electric screening scale.