In this paper, we use complexity equals action proposal and investigate the recently introduced ‘mutual complexity’ [M. Alishahiha, K. Babaei Velni and M. R. Mohammadi Mozaffar, Phys. Rev. D 99 (2019) 126016, https://doi.org/10.1103/PhysRevD.99.126016 , arXiv:1809.06031 [hep-th]], in the hyperscaling violating backgrounds. For two subregions in order to define holographic complexity, we find the finite bulk action inside the subregions which is followed by introducing the proper counter terms. We show that for two subregions, the mutual complexity is subadditive. Moreover, for three subregions, we define holographic ‘tripartite complexity’ and show that this new quantity is superadditive.

中文翻译：

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超大规模违反背景中的“相互复杂性”

在本文中，我们使用复杂性等于行动建议并研究最近引入的“相互复杂性”[M. Alishahiha，K. Babaei Velni 和 MR Mohammadi Mozaffar，Phys。Rev. D 99 (2019) 126016, https://doi.org/10.1103/PhysRevD.99.126016 , arXiv:1809.06031 [hep-th]]，在超大规模违反背景下。对于两个子区域，为了定义全息复杂性，我们发现子区域内的有限体积作用，然后引入适当的反项。我们表明，对于两个子区域，相互复杂性是次加性的。此外，对于三个子区域，我们定义了全息“三方复杂性”，并表明这个新量是超加性的。