arXiv 1104.24152011-04hep-thhep-phnucl-th

基于AdS/CFT的夸克-胶子等离子体瞬态流体动力学

Transient Fluid Dynamics of the Quark-Gluon Plasma According to AdS/CFT

Jorge Noronha, Gabriel S. Denicol

备注：: 11 pages, 1 figure: major changes in the text were made in order to clarify the discussion

摘要：

我们认为，使用AdS/CFT对应，在强耦合$\mathcal{N}=4$ SYM等离子体中的剪切应力张量的瞬态动力学不是由弛豫型流体动力学方程描述的：在很长的时间内，运动方程应该包含一个\textit{second-order}共动导数的剪切应力张量。这是因为在这个强耦合系统中，与剪切应力相关的最低“非流体动力学”准正规模式在零波数处具有非零实部。我们使用外尔不变性，以获得最一般的运动方程包含2个共动导数的剪切应力张量在瞬态制度，是兼容的对称性。我们表明，这个理论的渐近解有效的时间远大于与“非流体动力学”模式的时间尺度再现了众所周知的结果，以前直接从AdS/CFT对应。如果在重离子碰撞中形成的QGP可以至少定性地理解的强耦合$\mathcal{N}=4$ SYM理论，二阶时间导数存在于流体的运动方程可能会导致一个意想不到的依赖于初始条件的剪应力张量在数值流体动力学模拟中所需的。

英文摘要：

We argue, using the AdS/CFT correspondence, that the transient dynamics of the shear stress tensor in a strongly coupled $\mathcal{N}=4$ SYM plasma is not described by relaxation-type, fluid dynamical equations: at long times the equations of motion should contain a \textit{second-order} comoving derivative of the shear stress tensor. This occurs because in this strongly-coupled system the lowest "non-hydrodynamical" quasinormal modes associated with shear stress possess a nonzero real part at zero wavenumber. We use Weyl invariance to obtain the most general equations of motion containing 2 comoving derivatives of the shear stress tensor in the transient regime that are compatible with the symmetries. We show that the asymptotic solution of this theory valid at times much larger than the timescale associated with the "non-hydrodynamical" modes reproduces the well-known results previously obtained directly from the AdS/CFT correspondence. If the QGP formed in heavy ion collisions can be at least qualitatively understood in terms of strongly-coupled $\mathcal{N}=4$ SYM theory, the second time derivative present in the equations of motion of the fluid may lead to an unexpected dependence on the initial conditions for the shear stress tensor needed in numerical hydrodynamic simulations.

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