论文标题
纠缠从量子物质到经典几何形状的转移，在标量场理论的新兴全息二重述中
Entanglement transfer from quantum matter to classical geometry in an emergent holographic dual description of a scalar field theory
论文作者
论文摘要
将递归的重新归一化组转换应用于标量场理论时，我们获得了有效的量子重力理论，其出现额外的维度，由双重全息爱因斯坦 - 克莱因 - 凯莱因 - 戈登型动作描述。在这里，在递归递归的恢复量化组转换中，双重订单参数场和度量张量场的动力学分别来自密度密度和能量量张量的有效相互作用。重力部门的递归递归重新归一化组转换中的线性近似导致沿$ z- $定向的新兴空间的线性量子爱因斯坦量表理论。在大$ n $限制中，$ n $是原始标量字段的风味数量，抑制了动态度量标准和双标量表字段的量子波动，从而导致Einstein-Scalar类型的经典字段理论$（d+1）$ - spacetime尺寸。我们表明，这种新兴的背景重力描述了通过额外的维度在UV量子场理论中耦合函数的重新归一化组流。更准确地说，重力方程的IR边界条件对应于量子场理论的重新归一化组$β$函数，其中，超二维空间中的无穷小距离均以重新归一化组变换的能量尺度鉴定。最后，我们还表明，这种双重全息表述以几何方式描述了量子纠缠，编码量子纠缠从量子物质到经典重力的转移以$ n $限制。我们声称，这种纠缠转移是紧急全息二元描述的微观基础。
Applying recursive renormalization group transformations to a scalar field theory, we obtain an effective quantum gravity theory with an emergent extra dimension, described by a dual holographic Einstein-Klein-Gordon type action. Here, the dynamics of both the dual order-parameter field and the metric tensor field originate from density-density and energy-momentum tensor-tensor effective interactions, respectively, in the recursive renormalization group transformation, performed approximately in the Gaussian level. This linear approximation in the recursive renormalization group transformation for the gravity sector gives rise to a linearized quantum Einstein-scalar theory along the $z-$directional emergent space. In the large $N$ limit, where $N$ is the flavor number of the original scalar fields, quantum fluctuations of both dynamical metric and dual scalar fields are suppressed, leading to a classical field theory of the Einstein-scalar type in $(D+1)$-spacetime dimensions. We show that this emergent background gravity describes the renormalization group flows of coupling functions in the UV quantum field theory through the extra dimension. More precisely, the IR boundary conditions of the gravity equations correspond to the renormalization group $β$-functions of the quantum field theory, where the infinitesimal distance in the extra-dimensional space is identified with an energy scale for the renormalization group transformation. Finally, we also show that this dual holographic formulation describes quantum entanglement in a geometrical way, encoding the transfer of quantum entanglement from quantum matter to classical gravity in the large $N$ limit. We claim that this entanglement transfer serves as a microscopic foundation for the emergent holographic duality description.
