We show that the ideal fluid local equilibrium limit, defined as the existence of a flow frame \(u_\mu \) which characterises the direction of both a conserved entropy current and conserved charge currents is incompatible with non-Abelian gauge theory if local color charge density is non-zero. Instead, the equation of state becomes dependent on \(u_\mu \) via modes which are roughly equivalent to ghost modes in the hydrodynamic limit. These modes can be physically imagined as a field of “purcell swimmers” whose “arms and legs” are outstretched in Gauge space. Also, vorticity should couple to the Wilson loop via the chromo-electro-magnetic field tensor, which in local equilibrium is not a “force” but instead represents the polarization tensor of the gluons. We show that because of this coupling vorticity also acquires swirling non-hydrodynamic modes. We then argue that these swirling and swimming non-hydrodynamic modes are the manifestation of gauge redundancy within local equilibrium, and speculate on their role in quark-gluon plasma thermalization.

中文翻译：

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理想流体动力极限和非阿贝尔规范的对称性

我们表明，理想的流体局部平衡极限（定义为流框架\（u_ \ mu \）的存在）表征了熵流和守恒电荷流的方向，如果局部颜色与非阿贝尔规范理论不相容电荷密度不为零。相反，状态方程变得取决于\（u_ \ mu \）通过模式，该模式在流体动力极限中大致相当于幻影模式。这些模式在物理上可以想象为“赛艇游泳者”的领域，其“手臂和腿部”在仪表空间中伸出。同样，涡旋应该通过色度-电磁场张量耦合到威尔逊环，在局部平衡中它不是一个“力”，而是代表胶子的极化张量。我们表明，由于这种耦合，涡度也获得了涡旋非流体动力模式。然后，我们认为这些旋涡和游动非流体动力学模式是局部平衡内量规冗余的表现，并推测了它们在夸克-胶子等离子体热化中的作用。