Complexity-action of subregions with corners

TL;DR

This paper investigates the UV divergence structure of holographic subregion complexity-action in regions with corners, revealing universal divergences and the importance of counter terms for invariance and clarity.

Contribution

It develops a systematic method to analyze divergence structures in subregion CA, highlighting the role of counter terms and identifying universal divergence features.

Findings

Universal $ ext{log}\delta$ divergence associated with corners.

A general form of subregion CA includes volume and area contributions.

Difference between complexity prescriptions highlighted by area term presence.

Abstract

In the past, the study of the divergence structure of the holographic entanglement entropy on singular boundary regions uncovered cut-off independent coefficients. These coefficients were shown to be universal and to encode important field theory data. Inspired by these lessons we study the UV divergences of subregion complexity-action (CA) in a region with corner (kink). We develop a systematic approach to study all the divergence structures, and we emphasize that the counter term that restores reparameterization invariance on the null boundaries plays a crucial role in simplifying the results and rendering them more transparent. We find that a general form of subregion CA contains a part dependent on the null generator normalizations and a part that is independent of them. The former includes a volume contribution as well as an area contribution. We comment on the origin of the area term as entanglement entropy, and point out that its presence constitutes a robust difference between the two prescriptions to calculate subregion complexity (-action v.s. -volume). We also find universal $\log\delta$ divergence associated with the kink feature of the subregion. Similar flat angle limit as the subregion-CV result is obtained.