论文标题
LIFSHITZ动作的紧急几何形状和路径积分优化
Emergent geometry and path integral optimization for a Lifshitz action
论文作者
论文摘要
Caputa等人介绍的二维形成共形场理论的欧几里得路径积分的背景度量优化程序。 （Phys。Rev.Lett。119，071602（2017）），到$ z = 2 $各向异性尺度不变$（2+1）$ -Dimensional Lifshitz fielshits field fieldless field ofless scalials field theory overless scalive field，我们找到了用于静态和动力相关功能的最佳几何形状。对于静态相关函数，最佳背景度量等同于繁殖贴片上的ADS度量，而对于动态相关函数，我们发现LifShitz如Metric。该结果表明，类似Mera的张量网络，也许没有单位性，仍将被认为是该系统的数值描述的最佳背景时空配置，即使我们以我们开头的经典动作不是保构磁场理论。
Extending the background metric optimization procedure for Euclidean path integrals of two-dimensional conformal field theories, introduced by Caputa et al. (Phys. Rev. Lett. 119, 071602 (2017)), to a $z=2$ anisotropically scale-invariant $(2+1)$-dimensional Lifshitz field theory of a free massless scalar field, we find optimal geometries for static and dynamic correlation functions. For the static correlation functions, the optimal background metric is equivalent to an AdS metric on a Poincare patch, while for dynamical correlation functions, we find Lifshitz like metric. This results suggest that a MERA-like tensor network, perhaps without unitarity, would still be considered an optimal background spacetime configuration for the numerical description of this system, even though the classical action we start with is not a conformal field theory.
