论文标题
不均匀CFT中路径积分的几何形状和复杂性
Geometry and Complexity of Path Integrals in Inhomogeneous CFTs
论文作者
论文摘要
在这项工作中，我们在一类不均匀的2D CFT中开发了路径积分优化，该cfts通过将普通的CFT放在具有依赖位置度量的空间上而构建。在设置和解决一般优化问题之后，我们研究了包括Möbius，SSD和Rainbow变形CFT在内的特定示例，并分析了这些模型中通用状态类别的路径积分几何形状和复杂性。我们发现，最佳路径积分的指标与$ ads_3 $几何形状的特定切片相吻合，爱因斯坦的方程在其上等同于最小路径积分复杂性的条件。我们还发现，虽然路径积分复杂性的领先差异保持不变，但恒定贡献会以普遍的，依赖性的方式改变。此外，我们分析了不均匀的CFT中的纠缠熵，并表明它们满足了山的方程，这些方程可用于提取与第一条纠缠法一致的能量密度。我们的发现不仅支持散装空间切片和路径积分电路之间的比较，而且还证明了路径积分的几何形状和复杂性是理解不均匀系统有趣物理的强大工具。
In this work we develop the path integral optimization in a class of inhomogeneous 2d CFTs constructed by putting an ordinary CFT on a space with a position dependent metric. After setting up and solving the general optimization problem, we study specific examples, including the Möbius, SSD and Rainbow deformed CFTs, and analyze path integral geometries and complexity for universal classes of states in these models. We find that metrics for optimal path integrals coincide with particular slices of $AdS_3$ geometries, on which Einstein's equations are equivalent to the condition for minimal path integral complexity. We also find that while leading divergences of path integral complexity remain unchanged, constant contributions are modified in a universal, position dependent manner. Moreover, we analyze entanglement entropies in inhomogeneous CFTs and show that they satisfy Hill's equations, which can be used to extract the energy density consistent with the first law of entanglement. Our findings not only support comparisons between slices of bulk spacetimes and circuits of path integrations, but also demonstrate that path integral geometries and complexity serve as a powerful tool for understanding the interesting physics of inhomogeneous systems.
