‘Mutual complexity’ in hyperscaling violating background

Abstract

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.