# Holographic Fidelity Susceptibility

## TL;DR

This paper investigates holographic fidelity susceptibility in field theories with gravitational duals by analyzing the back reaction of a massive scalar field on the geometry, linking it to the volume difference of extremal slices.

## Contribution

It introduces a method to compute holographic fidelity susceptibility using volume differences in geometries affected by scalar field back reaction.

## Key findings

- Fidelity susceptibility relates to volume differences in extremal slices.
- Back reaction of scalar fields modifies the dual geometry.
- The approach connects field theory deformations to geometric measures.

## Abstract

For a field theory with a gravitational dual, we study holographic fidelity susceptibility for two states related by a deformation of a relevant operator. To do so, we study back reaction of a massive scalar field on the asymptotic behavior of the metric in an Einstein gravity coupled to a massive scalar field. Identifying the two states, holographically, with the original and back reacted geometries, the corresponding holographic fidelity susceptibility is given by the difference of the volume of an extremal time slice evaluated on the original and back reacted geometries.