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Realizations of the holographic correspondence in String/M theory typically involve spacetimes of the form $AdS \times Y$ where $Y$ is some internal space which geometrizes an internal symmetry of the dual field theory, hereafter referred to as an "$R$ symmetry". It has been speculated that areas of Ryu-Takayanagi surfaces anchored on the boundary of a subregion of $Y$, and smeared over the base space of the dual field theory, quantify entanglement of internal degrees of freedom. A natural candidate for the corresponding operators are linear combinations of operators with definite $R$ charge with coefficients given by the "spherical harmonics'' of the internal space: this is natural when the product spaces appear as IR geometries of higher dimensional AdS spaces. We study clustering properties of such operators both for pure $AdS \times Y$ and for flow geometries, where $AdS \times Y$ arises in the IR from a different spacetime in the UV, for example higher dimensional AdS or asymptotically flat spacetime. We show, in complete generality, that the two point functions of such operators separated along the internal space obey clustering properties at scales larger than the $AdS$ scale. For non-compact $Y$, this provides a notion of approximate locality. When $Y$ is compact, clustering happens only when the size of $Y$ is parametrically larger than the $AdS$ scale. This latter situation is realized in flow geometries where the product spaces arise in the IR from an asymptotically AdS geometry at UV, but not typically when they arise near black hole horizons in asymptotically flat spacetimes. We discuss the significance of this result for entanglement and comment on the role of color degrees of freedom., Comment: 24 pages, no figures

We explore perturbative corrections to quantum information geometry. In particular, we study a Bures information metric naturally associated with the correlation functions of a conformal field theory. We compute the metric of holographic four-point functions and include corrections generated by tree Witten diagrams in the bulk. In this setting, we translate properties of correlators into the language of information geometry. Cross terms in the information metric encode non-identity operators in the OPE. We find that the information metric is asymptotically AdS. Finally, we discuss an information metric for transition amplitudes., Comment: 18 pages, no figures; v2: typos fixed, transition amplitude discussion refined

We refine an earlier introduced 5-dimensional gravity solution capable of holographically capturing several qualitative aspects of (lattice) QCD in a strong magnetic background such as the anisotropic behaviour of the string tension, inverse catalysis at the level of the deconfinement transition or sensitivity of the entanglement entropy to the latter. Here, we consistently modify our solution of the considered Einstein-Maxwell-dilaton system to not only overcome an unphysical flattening at large distances in the quark-antiquark potential plaguing earlier work, but also to encapsulate inverse catalysis for the chiral transition in the probe approximation. This brings our dynamical holographic QCD model yet again closer to a stage at which it can be used to predict magnetic QCD quantities not directly computable via lattice techniques., Comment: 15 pages, 23 figures, major revision in the chiral part, appendices added, accepted for publication in PRD

We extend previous work on dynamical AdS/QCD models by introducing an extra ingredient under the form of a background magnetic field, this to gain insight into the influence such field can have on crucial QCD observables. Therefore, we construct a closed form analytic solution to an Einstein-Maxwell-dilaton system with a magnetic field. We specifically focus on the deconfinement transition, reporting inverse magnetic catalysis, and on the string tension, reporting a weaker/stronger confinement along/perpendicular to the magnetic field. The latter, being of importance to potential modelling of heavy quarkonia, is in qualitative agreement with lattice findings., Comment: 13 pages, 18 figures, references and appendix added, minor changes and improved discussion, published version

In this paper, we explore the connection between the curvature of the background De Sitter space-time with the spectroscopic study of entanglement of two atoms. Our set up is in the context of an Open Quantum System (OQS), where the two atoms, each having two energy levels and represented by Pauli spin tensor operators projected along any arbitrary direction. The system mimics the role of a pair of freely falling Unruh De-Witt detectors, which are allowed to non-adiabatically interact with a conformally coupled massless probe scalar field which has the role of background thermal bath. The effective dynamics of this combined system takes into account of the non-adiabatic interaction, which is commonly known as the Resonant Casimir Polder Interaction (RCPI) with the thermal bath. Our analysis reveals that the RCPI of two stable entangled atoms in the quantum vacuum states in OQS depends on the de Sitter space-time curvature relevant to the temperature of the thermal bath felt by the static observer. We also find that, in OQS, RCPI produces a new significant contribution appearing in the effective Hamiltonian of the total system and thermal bath under consideration. We find that the Lamb Shift is characterized by a decreasing inverse square power-law behavior, $L^{-2}$, when inter atomic Euclidean distance, $L$, is much larger than a characteristic length scale, $k$, which is the inverse surface gravity of the background De Sitter space. If the background space-time would have been Minkowskian this shift decreases as, $L^{-1}$, and is independent of temperature. Thus, we establish a connection between the curvature of the De Sitter space-time with the Lamb Shift spectroscopy., Comment: 65 pages, 3 figures, 1 Table, This project is the part of the non-profit virtual international research consortium "Quantum Structures of the Space-Time & Matter". Accepted for publication in European Physical Journal C