Volume complexity for Janus AdS3 geometries

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.

Automated summary

In this study, we investigated the relationship between complexity and volume in Janus AdS(3) geometries, finding that complexity becomes temperature-dependent in the presence of defects. For the time-dependent Janus BTZ black hole, the couplings of the entangled CFTs do not affect the complexity rate when equilibrium is restored. Additionally, the complexity rate for the out-of-equilibrium system is always smaller compared to the pure BTZ black hole background.