Divergences in the rate of complexification
High Energy Physics - Theory
2018-05-30 v1
Abstract
It is conjectured that the average energy provides an upper bound on the rate at which the complexity of a holographic boundary state grows. In this paper, we perturb a holographic CFT by a relevant operator with a time-dependent coupling, and study the complexity of the time-dependent state using the \textit{complexity equals action} and the \textit{complexity equals volume} conjectures. We find that the rate of complexification according to both of these conjectures has UV divergences, whereas the instantaneous energy is UV finite. This implies that neither the \textit{complexity equals action} nor \textit{complexity equals volume} conjecture is consistent with the conjectured bound on the rate of complexification.
Keywords
Cite
@article{arxiv.1712.07137,
title = {Divergences in the rate of complexification},
author = {Mudassir Moosa},
journal= {arXiv preprint arXiv:1712.07137},
year = {2018}
}