  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.
