# Holographic complexity: A tool to probe the property of reduced fidelity susceptibility

## TL;DR

This paper provides a quantitative proof of the duality between reduced fidelity susceptibility and holographic complexity, explores properties of holographic complexity in AdS3, and discusses potential experimental verification of the duality.

## Contribution

The paper offers the first quantitative proof of the RFS/HC duality and derives new properties of holographic complexity in AdS3, with implications for experimental tests.

## Key findings

- Established a quantitative proof of the RFS/HC duality.
- Derived important properties of holographic complexity in AdS3.
- Proposed experimental verification methods for the duality.

## Abstract

Quantum information theory along with holography play central roles in our understanding of quantum gravity. Exploring their connections will lead to profound impacts on our understanding of the modern physics and is thus a key challenge for present theory and experiments. In this paper, we investigate a recent conjectured connection between reduced fidelity susceptibility and holographic complexity (the RFS/HC duality for short). We give a quantitative proof of the duality by performing both holographic and field theoretical computations. In addition, holographic complexity in $AdS_{2+1}$ are explored and several important properties are obtained. These properties allow us, via the RFS/HC duality, to obtain a set of remarkable identities of the reduced fidelity susceptibility, which may have significant implications for our understanding of the reduced fidelity susceptibility. Moreover, utilizing these properties and the recent proposed diagnostic tool based on the fidelity susceptibility, experimental verification of the RFS/HC duality becomes possible.