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Fundamental interactions of nature are described by quantum gauge theories. The only exception is gravity, since its microscopic theory is not known yet. However quantum gravity would be significant to describe several fundamental phenomena, for example the thermodynamics of black holes. Several different theories have emerged to solve this problem, for example ones which propose that the fabric of spacetime is held together by the entanglement of certain quantum states. A breakthrough in the quantum mechanical description of gravity is provided by the AdS/CFT correspondence, which, in its original form, establishes a connection between quantum strings moving on a anti-de Sitter background and a dual, gravity-free conformal field theory living on the boundary of the AdS space.
Since its original formulation, the AdS/CFT duality has appeared in various contexts. One exceptional result is the so-called Ryu-Takayanagi relation, which states that the area of minimal surfaces in any-dimensional asymptotically anti-de Sitter space is proportional to the entanglement entropies of corresponding regions in the conformal field theory living on the one-dimension-lower boundary of the space. The RT relation uses the tools of the AdS/CFT correspondence to relate geometry and entanglement.
In our research we have reached back to the original statement of the AdS/CFT correspondence and used the RT formula to relate the geometry of AdS strings to boundary entanglement. We have investigated a special approximation of string worldsheets and given a precise way to uniquely project them to the boundary. Using the RT formula we were able to show that their area is proportional to a special combination of the entanglement entropies of certain CFT boundary subsystems in vacuum state.
In my presentation I am going to give a brief intorduction to the entanglement context of the AdS/CFT correspondence and summarize our recent results about segmented strings and holography.