Volume complexity for Janus $\mathrm{AdS}_3$ geometries

TL;DR

This paper explores the volume complexity in Janus AdS$_3$ geometries, revealing a logarithmic divergence linked to the interface, and examines how complexity evolves with temperature and time, especially in out-of-equilibrium states.

Contribution

It introduces the analysis of volume complexity in Janus AdS$_3$ geometries at finite temperature and during time evolution, highlighting the effects of the interface and coupling differences.

Findings

Logarithmic divergence in complexity from the Janus interface.

Complexity becomes temperature-dependent in the presence of defects.

Out-of-equilibrium complexity rate is lower than in pure BTZ black holes.

Abstract

We investigate the complexity=volume proposal in the case of Janus AdS$_3$ geometries, both at zero and finite temperature. The leading contribution coming from the Janus interface is a logarithmic divergence, whose coefficient is a function of the dilaton excursion. In the presence of the defect, complexity is no longer topological and becomes temperature-dependent. We also study the time evolution of the extremal volume for the time-dependent Janus BTZ black hole. This background is not dual to an interface but to a pair of entangled CFTs with different values of the couplings. At late times, when the equilibrium is restored, the couplings of the CFTs do not influence the complexity rate. On the contrary, the complexity rate for the out-of-equilibrium system is always smaller compared to the pure BTZ black hole background.