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有限耦合下的流体力学色散关系

Hydrodynamic dispersion relations at finite coupling

Sašo Grozdanov, Andrei O. Starinets, Petar Tadić

备注：
47 pages, 23 figures
发表信息：
JHEP 2106 (2021) 180
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AI总结：

本文将全息方法对 $\mathcal{N}=4$ 超对称 Yang-Mills 理论流体力学色散关系收敛半径的计算从无限耦合推广到有限耦合，发现非微扰效应使收敛半径对耦合的依赖呈分段连续，并用 Einstein-Gauss-Bonnet 引力模型验证了该行为。

摘要：

此前，利用全息方法，已在无限大 't Hooft 耦合和无限大颜色数条件下计算了 ${\cal N} = 4$ 超对称 Yang-Mills 理论中流体力学剪切模和声模色散关系的收敛半径。本文将该分析扩展到 't Hooft 耦合为大但有限的情形。在微扰展开的领头阶，我们发现收敛半径随逆耦合的增大而增大，这与朴素预期相反。然而，当利用一种定性的非微扰重求和方案求解运动方程时，对耦合的依赖变为分段连续，初始的增长之后随之出现下降。这种分段连续依赖性与能动张量有限温度两点函数在空间动量平方复平面中分支点奇点的动力学有关。我们进一步以 Einstein-Gauss-Bonnet 引力为模型重复了该研究，在该模型中方程可以被完全非微扰地求解，并发现收敛半径随有效逆耦合的减小符合预期，且同样呈现分段连续行为。最后，我们给出了支持非微扰方法的论证，并表明准正规谱中非微扰模式的存在可以通过对微扰临界点的分析间接推断出来。

英文摘要：

By using holographic methods, the radii of convergence of the hydrodynamic shear and sound dispersion relations were previously computed in the ${\cal N} = 4$ supersymmetric Yang-Mills theory at infinite 't Hooft coupling and infinite number of colours. Here, we extend this analysis to the domain of large but finite 't Hooft coupling. To leading order in the perturbative expansion, we find that the radii grow with increasing inverse coupling, contrary to naive expectations. However, when the equations of motion are solved using a qualitative non-perturbative resummation, the dependence on the coupling becomes piecewise continuous and the initial growth is followed by a decrease. The piecewise nature of the dependence is related to the dynamics of branch point singularities of the energy-momentum tensor finite-temperature two-point functions in the complex plane of spatial momentum squared. We repeat the study using the Einstein-Gauss-Bonnet gravity as a model where the equations can be solved fully non-perturbatively, and find the expected decrease of the radii of convergence with the effective inverse coupling which is also piecewise continuous. Finally, we provide arguments in favour of the non-perturbative approach and show that the presence of non-perturbative modes in the quasinormal spectrum can be indirectly inferred from the analysis of perturbative critical points.

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