# Fidelity susceptibility for Lifshitz geometries via Lifshitz Holography

## TL;DR

This paper extends holographic methods to compute fidelity susceptibility in non-relativistic Lifshitz geometries, linking bulk gravity theories with condensed matter systems and demonstrating the approach with explicit examples.

## Contribution

It introduces a holographic proposal for fidelity susceptibility in Lifshitz geometries and applies it to a non-relativistic many-body system, showing the correspondence.

## Key findings

- Fidelity susceptibility can be holographically obtained from Lifshitz geometries.
- The approach is validated using Einstein-Dilaton-Maxwell-AdS-Lifshitz theory.
- Fidelity susceptibility of a bosonic system matches the bulk calculation.

## Abstract

In order to analyze the fidelity susceptibility of non-relativistic field theories, which are important in condensed matter systems, we generalize the proposal to obtain the fidelity susceptibility holographically to Lifshitz geometries. It will be argued that this proposal can be used to study the fidelity susceptibility for various condensed matter systems. To demonstrated this, we will explicitly use this proposal to analyze the fidelity susceptibility for a non-relativistic many-body system, and argue that the fidelity susceptibility of this theory can be holographically obtained from a bulk Lifshitz geometry. In fact, using a Einstein-Dilaton-Maxwell-AdS-Lifshitz theory, we explicitly demonstrated that the fidelity susceptibility obtained from this bulk geometry is equal to the fidelity susceptibility of a bosonic many-body system.