边界能区分复杂性吗？
Does Boundary Distinguish Complexities?
摘要：
最近，查普曼等人认为，缺陷的全息复杂性将作用与体积区分开来。受他们工作的启发，我们研究了有边界共形场论中量子态的复杂性。在一般的二维BCFT中，我们研究了路径积分优化，它给出了复杂性的场论定义之一。我们还进行了高柳的AdS/BCFT模型的复杂性的全息计算，随后的“复杂性$=$体积”猜想和“复杂性$=$行动”猜想。我们发现，除了AdS $_3$ /BCFT $_2$模型的CA复杂性与Chapman等人的观点不同外，边界引起的复杂性增量在这些模型中表现出相同的发散结构，因此，我们得出结论，边界并不能区分一般的复杂性。
英文摘要：
Recently, Chapman et al. argued that holographic complexities for defects distinguish action from volume. Motivated by their work, we study complexity of quantum states in conformal field theory with boundary. In generic two-dimensional BCFT, we work on the path-integral optimization which gives one of field-theoretic definitions for the complexity. We also perform holographic computations of the complexity in Takayanagi's AdS/BCFT model following by the "complexity $=$ volume" conjecture and "complexity $=$ action" conjecture. We find that increments of the complexity due to the boundary show the same divergent structures in these models except for the CA complexity in the AdS$_3$/BCFT$_2$ model as the argument by Chapman et al. Thus, we conclude that boundary does not distinguish the complexities in general.
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