论文标题
保形场理论中复杂性的几何形状
Geometry of Complexity in Conformal Field Theory
论文作者
论文摘要
我们启动了（1+1） - 维构理论中复杂性的定量研究，以表明它们提供了最简单的设置，以找到重力双重二重要的复杂性。我们的工作追求对保形转换的复杂性的几何理解，并嵌入了Fubini研究状态的复杂性，并直接计数应力张量插入相关电路中的压力张量。在前一种情况下，我们迭代地求解了样品最佳电路的新出现的全差异方程，并讨论了基础几何形状的截面曲率。在后一种情况下，我们认识到，最佳电路受Euler-Arnold类型方程的控制，并在复杂性的背景下讨论了此类型的三个知名方程的相关结果。
We initiate quantitative studies of complexity in (1+1)-dimensional conformal field theories with a view that they provide the simplest setting to find a gravity dual to complexity. Our work pursues a geometric understanding of complexity of conformal transformations and embeds Fubini-Study state complexity and direct counting of stress tensor insertion in the relevant circuits in a unified mathematical language. In the former case, we iteratively solve the emerging integro-differential equation for sample optimal circuits and discuss the sectional curvature of the underlying geometry. In the latter case, we recognize that optimal circuits are governed by Euler-Arnold type equations and discuss relevant results for three well-known equations of this type in the context of complexity.
