Is volume the holographic dual of fidelity susceptibility?

TL;DR

This paper investigates the proposed holographic duality between volume and fidelity susceptibility in conformal field theories, finding structural similarities but numerical inconsistencies in their divergences.

Contribution

The study critically examines the proposed duality by analyzing divergence structures, revealing discrepancies that challenge the exactness of the conjectured relationship.

Findings

Divergence structures are similar in both quantities.

Numerical coefficients do not match exactly.

The proposed duality may not be exact.

Abstract

It was proposed by Miyaji et al. that the fidelity susceptibility of a state of a conformal field theory under a marginal deformation is holographically dual to the volume of a maximal time slice in the dual Anti de Sitter spacetime. We study this proposal by analyzing the leading and subleading divergences in these two quantities in two specific scenarios. We find that although the structure of the divergences in these two quantities is similar, their numerical coefficients are inconsistent with an exact relationship between these two quantities.