Holographic entanglement entropy, complexity, fidelity susceptibility and hierarchical UV/IR mixing problem in AdS2/open strings

Abstract

In this paper, we will compute the holographic complexity (dual to a volume in AdS), holographic fidelity susceptibility and the holographic entanglement entropy (dual to an area in AdS) in a two-dimensional version of AdS which is dual to open strings. We will explicitly demonstrate that these quantities are well defined, and then argue that a relation for fidelity susceptibility and time should hold in general due to the AdS2 version of the classical Kepler’s principle. We will demonstrate that it holds for AdS2 solution as well as conformal copies metrics in bulk theory of a prescribed dual conformal invariant quantum mechanics which have been obtained in open string theory. We will also show that hierarchical UV/IR mixing exists in boundary string theory through the holographic bulk picture.