Holographic complexity and fidelity susceptibility as holographic information dual to different volumes in AdS

N.S Mazhari,Ratbay Myrzakulov,Mir Faizal,Sebastian Bahamonde,Davood Momeni

doi:10.1016/j.physletb.2016.12.060

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.

Highlights

The information theory deals with the ability of an observer to process relevant information, and it is important as studies done in different branches of physics seem to indicated that the laws of physics are informational theoretical processes [1, 2]
It may be noted that the holographic complexity depends on the size of the subsystem l and as the fidelity susceptibility was calculated for the full system, no such dependence has been observed
The laws of physics can be represented in terms of the ability of an observer to process relevant information

Summary

Introduction

The information theory deals with the ability of an observer to process relevant information, and it is important as studies done in different branches of physics seem to indicated that the laws of physics are informational theoretical processes [1, 2]. It is interesting to note that the fidelity susceptibility of the boundary theory can be used for analyzing the quantum phase transitions [23, 24, 25], and it is possible to study quantum phase transitions holographically It is possible use a subsystem A with its complement, and define the volume as V = V (γ). These quantities calculated in the bulk could be used to understand the behavior of the boundary field theory dual to such geometries This is the main motivation to study such quantities for an AdSd+2 black hole, Janus solution, cylindrical solution, inhomogeneous backgrounds, and hyperscaling violating backgrounds. Apart from having interesting boundary duals, these solutions are interesting geometric solutions By calculating these quantities for these solutions, we will try to understand certain universal features of holographic complexity and fidelity susceptibility for different deformations of the AdS geometry.

AdS Black Holes

Janus Solution

Cylindrical Symmetry

Inhomogeneous Backgrounds

Hyperscaling Violating Backgrounds

Conclusion