# Subsystem complexity in warped AdS

## TL;DR

This paper analyzes the ultraviolet divergences of holographic subregion complexity in warped AdS$_3$ black holes, revealing new logarithmic divergences and their properties, and exploring the complexity's temperature dependence.

## Contribution

It provides the first detailed computation of UV divergences in subregion complexity for warped AdS$_3$, including the effects of logarithmic divergences and superadditivity.

## Key findings

- Logarithmic divergences appear alongside linear ones in warped AdS$_3$.
- Subregion action complexity is superadditive, regardless of counterterm choices.
- Complexity correlates with the sign of the specific heat at constant angular momentum.

## Abstract

We compute the ultraviolet divergences of holographic subregion complexity for the left and right factors of the thermofield double state in warped AdS$_3$ black holes, both for the action and the volume conjectures. Besides the linear divergences, which are also present in the BTZ black hole, additional logarithmic divergences appear. For the action conjecture, these log divergences are not affected by the arbitrarity in the length scale associated with the counterterm needed to ensure reparameterization invariance. We find that the subregion action complexity obeys the superadditivity property for the thermofield double in warped AdS$_3$, independently from the action counterterm coefficient. We study the temperature dependence of subregion complexity at constant angular momentum and we find that it is correlated with the sign of the specific heat.