The effect of Dilaton on the holographic complexity growth

TL;DR

This paper studies how the presence of a dilaton field affects the growth of holographic complexity in different black hole backgrounds, revealing violations of the Lloyd bound and new behaviors at late times.

Contribution

It provides a detailed analysis of action growth in Einstein-Maxwell-Dilaton backgrounds, including Lifshitz black holes, highlighting novel late-time behaviors and bound violations.

Findings

Action growth approaches late-time bound in AdS dilaton black holes

Lloyd bound is violated in Lifshitz black holes at late times

Full time behavior shows new features for large dynamical exponent z

Abstract

In this paper, we investigate the action growth in various backgrounds in Einstein-Maxwell-Dilaton theory. We calculate the full time evolution of action growth in AdS dilaton black hole and find it approaches the late time bound from above. We investigate the black hole which is asymptotically Lifshitz and obtain its late-time and full time behavior. We find the violation of Lloyd bound in late time limit and show the full time behavior exhibiting some new features for z sufficiently large.