Complexity Growth with Lifshitz Scaling and Hyperscaling Violation

TL;DR

This paper investigates the growth rate of holographic complexity in Lifshitz and hyperscaling violating geometries, revealing violations of Lloyd's bound and different saturation behaviors for one and two-sided black branes.

Contribution

It demonstrates that in Lifshitz and hyperscaling violating backgrounds, the complexity growth rate exceeds traditional bounds, providing new insights into holographic complexity in anisotropic spacetimes.

Findings

Lloyd's bound is violated in these geometries.

Complexity growth saturates above twice the black brane mass.

Saturation behavior differs between one and two-sided black branes.

Abstract

Using complexity=action proposal we study the growth rate of holographic complexity for Lifshitz and hyperscaling violating geometries. We will consider both one and two sided black branes in an Einstein-Maxwell-Dilaton gravitational theory. We find that in either case Lloyd's bound is violated and the rate of growth of complexity saturates to a value which is greater than twice the mass of the corresponding black brane. This value reduces to the mass of the black brane in the isotropic case. We show that in two sided black brane the saturation happens from above while for one sided black brane it happens from below.