复杂性第一定律
The First Law of Complexity
摘要：
我们研究了两个邻近目标态的全息复杂度的变化。基于Nielsen的几何方法，我们发现这种变化只依赖于最优轨迹的终点，这一结果我们命名为复杂性第一定律。作为一个例子，我们研究的复杂性=行动的猜想时，AdS真空扰动的标量场激发，这对应于一个相干态。值得注意的是，引力的贡献完全抵消，最后的变化减少到一个边界项完全来自标量场的行动。因此，Wheeler-DeWitt补丁的零边界看起来像是“量子线路的末端“。
英文摘要：
We investigate the variation of holographic complexity for two nearby target states. Based on Nielsen's geometric approach, we find the variation only depends on the end point of the optimal trajectory, a result which we designate the first law of complexity. As an example, we examine the complexity=action conjecture when the AdS vacuum is perturbed by a scalar field excitation, which corresponds to a coherent state. Remarkably, the gravitational contributions completely cancel and the final variation reduces to a boundary term coming entirely from the scalar field action. Hence the null boundary of Wheeler-DeWitt patch appears to act like the "end of the quantum circuit".
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