Segmented strings and holography

In this paper we establish a connection between segmented strings propagating in $AdS_{d+1}$ and $CFT_d$ subsystems in Minkowski spacetime characterized by quantum information theoretic quantities calculated for the vacuum state. We show that the area of the world sheet of a string segment on the AdS side can be connected to fidelity susceptibility (the real part of the quantum geometric tensor) on the CFT side. This quantity has another interpretation as the computational complexity for infinitesimally separated states corresponding to causal diamonds that are displaced in a spacelike manner according to the metric of kinematic space. These displaced causal diamonds encode information for a unique reconstruction of the string world sheet segments in a holographic manner. Dually the bulk segments are representing causally ordered sets of consecutive boundary events in boosted inertial frames or in noninertial ones proceeding with constant acceleration. For the special case of $AdS_3$ one can also see the segmented stringy area in units of $4GL$ ($G$ is Newton's constant and $L$ is the AdS length) as the conditional mutual information $I(A,C\vert B)$ calculated for a trapezoid configuration arising from boosted spacelike intervals $A$,$B$ and $C$. In this special case the variation of the discretized Nambu-Goto action leads to an equation for entanglement entropies in the boundary theory of the form of a Toda equation. For arbitrary $d$ the string world sheet patches are living in the modular slices of the entanglement wedge. They seem to provide some sort of tomography of the entanglement wedge where the patches are linked together by the interpolation ansatz, i.e. the discretized version of the equations of motion for the Nambu-Goto action.