Constraining nonrelativistic RG flows with holography
Constraining nonrelativistic RG flows with holography
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DOI：
10.1103/physrevd.103.046006
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发表时间：
2020-06
影响因子：
5
通讯作者：
S. Cremonini;Li Li-Li;Kyle Ritchie;Yuezhang Tang
中科院分区：
文献类型：
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作者：
S. Cremonini;Li Li-Li;Kyle Ritchie;Yuezhang Tang
我们研究非相对论全息重整化群（RG）流与爱因斯坦麦克斯韦标量理论，支持打破洛伦兹不变性的几何形状，在一定的能量尺度。我们采用超势的形式主义，这有助于我们描述径向流在这个设置，并带来一些通用功能。特别是，我们确定了几个数量的RG流下的单调行为。作为一个例子，我们表明，折射率一般是单调的。我们还构建了一个组合的超势流单调的爱因斯坦标量理论支持非相对论的解决方案，并减少到已知的c-函数的相对论极限。有趣的是，这样的量在爱因斯坦-麦克斯韦标量理论的各种黑洞解中也表现出单调性，暗示着更深层次的结构。最后，我们评论这种单调性条件的故障和先前从纠缠熵获得的候选c-函数的关系。
We examine nonrelativistic holographic renormalization group (RG) flows by working with Einstein-Maxwell-scalar theories which support geometries that break Lorentz invariance at some energy scale. We adopt the superpotential formalism, which helps us characterize the radial flow in this setup and bring to light a number of generic features. In particular, we identify several quantities that behave monotonically under RG flow. As an example, we show that the index of refraction is generically monotonic. We also construct a combination of the superpotentials that flows monotonically in Einstein-scalar theories supporting nonrelativistic solutions and which reduces to the known c-function in the relativistic limit. Interestingly, such quantity also exhibits monotonicity in a variety of black hole solutions to the full Einstein-Maxwell-scalar theory, hinting at a deeper structure. Finally, we comment on the breakdown of such monotonicity conditions and on the relation to a candidate c-function obtained previously from entanglement entropy.