Holographic Complexity of Subregions in the Hyperscaling Violating Theories

TL;DR

This paper explores holographic complexity in hyperscaling violating theories using the complexity equals action proposal, analyzing subregions of black brane spacetimes and revealing late-time independence from hyperscaling parameters.

Contribution

It extends previous holographic complexity calculations to hyperscaling violating geometries and introduces counter terms for finite action computation.

Findings

Late-time complexity growth rate is independent of hyperscaling parameters.

Dynamical exponent significantly influences the complexity rate.

Finite on-shell action is obtained with new counter terms.

Abstract

In this paper, we use the complexity equals action proposal and investigate holographic complexity for hyperscaling violating theories on different subregions of space-time enclosed by the null boundaries. We are interested in computing the onshell action for certain subregions of the intersection between the Wheeler DeWitt patch and the past, as well as, the future interior of a two-sided black brane. More precisely, we extend the results of Ref. \cite{Alishahiha:2018lfv} in parts, to hyperscaling violating geometries and to find the finite onshell action, we define the proper counter terms. We show that in computing the rate of complexification the dynamical exponent plays a crucial rule, but, at the late time, rate of the complexity growth is independent of the hyperscaling parameters.