Action complexity in the presence of defects and boundaries

TL;DR

This paper compares holographic complexity measures in AdS$_3$ models with defects and boundaries, showing that both volume and action proposals can yield similar divergences in certain cases, challenging previous assumptions.

Contribution

It demonstrates that the volume and action conjectures for holographic complexity can agree on divergence types in AdS$_3$ models with defects, specifically in Janus AdS$_3$.

Findings

Volume and action proposals show the same logarithmic divergences in Janus AdS$_3$.

Divergences differ in some models but can coincide in others.

Challenges the notion that divergences are always different for defects and boundaries.

Abstract

The holographic complexity of formation for the AdS$_3$ $2$-sided Randall-Sundrum model and the AdS$_3$/BCFT$_2$ models is logarithmically divergent according to the volume conjecture, while it is finite using the action proposal. One might be tempted to conclude that the UV divergences of the volume and action conjectures are always different for defects and boundaries in two-dimensional conformal field theories. We show that this is not the case. In fact, in Janus AdS$_3$ we find that both volume and action proposals provide the same kind of logarithmic divergences.