On the time dependence of holographic complexity in a dynamical Einstein-dilaton model

TL;DR

This paper investigates the time evolution of holographic complexity in Einstein-dilaton gravity, revealing dimension-dependent violations of the Lloyd bound with the CA proposal and consistent results with the CV proposal.

Contribution

It analytically constructs an infinite family of black hole solutions and compares the CA and CV proposals for holographic complexity in a dynamical Einstein-dilaton model.

Findings

Lloyd bound is violated in a dimension-dependent manner.

Early and late time complexity behaviors differ between CA and CV proposals.

Parameter tuning can control the extent of bound violation.

Abstract

We study the holographic "complexity=action'" (CA) and "complexity=volume" (CV) proposals in Einstein-dilaton gravity in all spacetime dimensions. We analytically construct an infinite family of black hole solutions and use CA and CV proposals to investigate the time evolution of the complexity. Using the CA proposal, we find dimensional dependent violation of the Lloyd bound in early as well as in late times. Moreover, depending on the parameters of the theory, the bound violation relative to the conformal field theory result can be tailored in the early times as well. In contrast to the CA proposal, the CV proposal in our model yields results similar to those obtained in the literature.