Holographic Fisher Information Metric in Schrödinger Spacetime

Abstract

In this paper we study the Fisher information metric on the space of the coupling constants on both sides of the duality between non-relativistic dipole field theories and string theory in Schrödinger spacetime. We consider the following setup. In the gauge theory side one can deform a given conformal field theory by a proper scalar operator and compute the quantum information metric via the two-point correlation function between two such operators. On the string side the deformation corresponds to a scalar field probing the background. In the large $N$ limit of the theory the probing can be done without backreaction on the original spacetime, thus one can construct a perturbative scheme for the calculation of the dual holographic Fisher information metric as shown by \cite{Trivella:2016brw}. Considering the asymptotic behaviour of the holographic Fisher information metric close to the boundary of the Schrödinger spacetime we show that its divergence structure exactly matches its dual quantum counterpart up to the leading order, thus extending the holographic setup up to the non-relativistic case. One should note that the existence of other terms are not seen from the boundary theory to this level of approximation. Their behaviour near the boundary however, is pointing what kind of information from the boundary theory is missing to be able to reconstruct the bulk. Obviously more work is needed to refine and elucidate their meaning and interrelations in holographic setup.

Minor corrections

References in corpus (13)

• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Complexity and Shock Wave Geometries
• Phase diagram of a two-component Fermi gas with resonant interactions
• Surface/State Correspondence as a Generalized Holography
• Correlation Functions in Non-Relativistic Holography
• Multispin Giant Magnons
• Hessian matrix, specific heats, Nambu brackets, and thermodynamic geometry
• Magnons, Classical Strings and beta-Deformations
• Spiky Strings, Giant Magnons and beta-deformations
• Thermodynamic Information Geometry and Complexity Growth of Warped AdS Black Hole and the WAdS${}_3$/CFT${}_2$ Correspondence
• Probing Universality in the Gravity Duals of N=1 SYM by gamma-deformations
• Informational properties of holographic Lifshitz field theory

Cited by in corpus (1)

• Giant Gravitons in the Schrodinger holography