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It was proposed by Miyaji et al. that the fidelity susceptibility of a stateof a conformal field theory under a marginal deformation is holographicallydual to the volume of a maximal time slice in the dual Anti de Sitterspacetime. We study this proposal by analyzing the leading and subleadingdivergences in these two quantities in two specific scenarios. We find thatalthough the structure of the divergences in these two quantities is similar,their numerical coefficients are inconsistent with an exact relationshipbetween these two quantities.

Is volume the holographic dual of fidelity susceptibility?