论文标题
在违反LIFSHITZ理论的高度标准中，剪切响应功能的流动
Flow of shear response functions in hyperscaling violating Lifshitz theories
论文作者
论文摘要
我们研究了违反LIFSHITZ（HVLIF）理论的剪切响应函数的流动方程，其中LIFSHITZ和超标准违反了指数$ z $和$θ$。调整膜范式的方法分析由IQBAL和LIU开发的响应函数的方法，我们专门关注剪切重力模式，该模式现在与背景量规场的扰动相结合。限制到零动量部门，我们就扰动的流体动力扩张做出了进一步的简单假设。分析流程方程表明，领先顺序的剪切粘度使$ \ frac {1} {4π} $的kovtun-son-Starinets（KSS）饱和。当$ z = d_i-θ$（$ d_i $是双场理论中的空间维度数）时，对剪切粘度的一阶校正表现出对数的缩放，这表明了此类HVLIF理论的UV制度中量表中的出现。我们进一步表明，当$ z> d_i+2-θ$时，与量规场扰动相关的响应函数会散开。这提供了对这种约束的起源的全息理解，并进一步证明了通过近距离和准标准分析获得的先前作品中获得的结果。
We study the flow equations of the shear response functions for hyperscaling violating Lifshitz (hvLif) theories, with Lifshitz and hyperscaling violating exponents $z$ and $θ$. Adapting the membrane paradigm approach of analysing response functions as developed by Iqbal and Liu, we focus specifically on the shear gravitational modes which now are coupled to the perturbations of the background gauge field. Restricting to the zero momenta sector, we make further simplistic assumptions regarding the hydrodynamic expansion of the perturbations. Analysing the flow equations shows that the shear viscosity at leading order saturates the Kovtun-Son-Starinets (KSS) bound of $\frac{1}{4π}$. When $z=d_i-θ$, ($d_i$ being the number of spatial dimension in the dual field theory) the first-order correction to shear viscosity exhibits logarithmic scaling, signalling the emergence of a scale in the UV regime for this class of hvLif theories. We further show that the response function associated to the gauge field perturbations diverge near the boundary when $z>d_i+2-θ$. This provides a holographic understanding of the origin of such a constraint and further vindicates results obtained in previous works that were obtained through near horizon and quasinormal mode analysis.
