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In this paper we study the Fisher information metric on the space of thecoupling constants on both sides of the duality between non-relativistic dipolefield theories and string theory in Schr\"odinger spacetime. We consider thefollowing setup. In the gauge theory side one can deform a given conformalfield theory by a proper scalar operator and compute the quantum informationmetric via the two-point correlation function between two such operators. Onthe string side the deformation corresponds to a scalar field probing thebackground. In the large $N$ limit of the theory the probing can be donewithout backreaction on the original spacetime, thus one can construct aperturbative scheme for the calculation of the dual holographic Fisherinformation metric as shown by \cite{Trivella:2016brw}. Considering theasymptotic behaviour of the holographic Fisher information metric close to theboundary of the Schr\"odinger spacetime we show that its divergence structureexactly matches its dual quantum counterpart up to the leading order, thusextending the holographic setup up to the non-relativistic case. One shouldnote that the existence of other terms are not seen from the boundary theory tothis level of approximation. Their behaviour near the boundary however, ispointing what kind of information from the boundary theory is missing to beable to reconstruct the bulk. Obviously more work is needed to refine andelucidate their meaning and interrelations in holographic setup.

Holographic Fisher Information Metric in Schr\"odinger Spacetime