Is volume the holographic dual of fidelity susceptibility?

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.

arXiv commentSec.(2) revised, minor changes to Sec.(3), appendix on bulk/boundary cutoffs added, references added

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• WdW-patches in AdS${}_3$ and complexity change under conformal transformations II
• Holographic entanglement entropy and complexity in St$\ddot{u}$ckelberg superconductor
• Holographic Fisher Information Metric in Schrödinger Spacetime