Holographic Complexity of Einstein-Maxwell-Dilaton Gravity

TL;DR

This paper investigates the holographic complexity in Einstein-Maxwell-Dilaton gravity with hyperscaling violation, analyzing action growth, switchback effect, and tensor network models to understand complexity dynamics.

Contribution

It introduces calculations of complexity growth in hyperscaling violating geometries and explores the switchback effect using shockwave geometries.

Findings

Action growth rate is enhanced with hyperscaling violation.

Switchback effect is demonstrated in shockwave geometries.

Tensor network models partially capture hyperscaling violation effects.

Abstract

We study the holographic complexity of Einstein-Maxwell-Dilaton gravity using the recently proposed "complexity = volume" and "complexity = action" dualities. The model we consider has a ground state that is represented in the bulk via a so-called hyperscaling violating geometry. We calculate the action growth of the Wheeler-DeWitt patch of the corresponding black hole solution at non-zero temperature and find that, in the presence of violations of hyperscaling, there is a parametric enhancement of the action growth rate. We partially match this behavior to simple tensor network models which can capture aspects of hyperscaling violation. We also exhibit the switchback effect in complexity growth using shockwave geometries and comment on a subtlety of our action calculations when the metric is discontinuous at a null surface.