Bath deformations, islands and holographic complexity

TL;DR

This paper investigates how bath deformations affect holographic subregion complexity during a renormalization group flow, revealing a discontinuous jump at Page time that depends on system parameters and scalar operator dimensions.

Contribution

It introduces a model analyzing the impact of relevant scalar operator deformations on holographic complexity during RG flow from AdS-Schwarzschild to Kasner universe.

Findings

Discontinuous jump in subregion complexity at Page time.

Discontinuity magnitude decreases with perturbation strength.

Discontinuity also decreases with scalar operator's scaling dimension.

Abstract

Considering a doubly holographic model, we study the evolution of holographic subregion complexity corresponding to deformations of bath state by a relevant scalar operator, which corresponds to a renormalization group flow from the AdS-Schwarzschild to the Kasner universe in the bulk. The subregion complexity shows a discontinuous jump at Page time at a fixed perturbation, where the discontinuity depends solely on the system's parameters. We show that the amount of discontinuity decreases with the perturbation as well as with the scaling dimension of the relevant scalar operator.