Holographic Complexity and Fidelity Susceptibility as Holographic Information Dual to Different Volumes in AdS

TL;DR

This paper explores holographic complexity and fidelity susceptibility as dual quantities to different volumes in AdS, calculating them for various deformations and backgrounds to understand their dependence on subsystem size.

Contribution

It introduces calculations of holographic complexity and fidelity susceptibility for diverse AdS deformations, highlighting their different dependencies on subsystem size.

Findings

Holographic complexity depends on subsystem size across all solutions.

Fidelity susceptibility shows no dependence on subsystem size.

Results apply to black holes, Janus solutions, and inhomogeneous backgrounds.

Abstract

The holographic complexity and fidelity susceptibility have been defined as new quantities dual to different volumes in AdS. In this paper, we will use these new proposals to calculate both of these quantities for a variety of interesting deformations of AdS. We obtain the holographic complexity and fidelity susceptibility for an AdS black hole, Janus solution and a solution with cylindrically symmetry, an inhomogeneous background and a hyperscaling violating background. It is observed that the holographic complexity depends on the size of the subsystem for all these solutions and the fidelity susceptibility does not have any such dependence.