Page curve for entanglement negativity through geometric evaporation

We compute the entanglement negativity for various pure and mixed state configurations in a bath coupled to an evaporating two dimensional non-extremal Jackiw-Teitelboim (JT) black hole obtained through the partial dimensional reduction of a three dimensional BTZ black hole. Our results exactly reproduce the analogues of the Page curve for the entanglement negativity which were recently determined through diagrammatic technique developed in the context of random matrix theory.

Anomalies as obstructions: from dimensional lifts to swampland

We revisit the relation between the anomalies in four and six dimensions and the Chern-Simons couplings one dimension below. While the dimensional reduction of chiral theories is well-understood, the question which three and five-dimensional theories can come from a general circle reduction, and are hence liftable, is more subtle. We argue that existence of an anomaly cancellation mechanism is a necessary condition for liftability. In addition, the anomaly cancellation and the CS couplings in six and five dimensions respectively determine the central charges of string-like BPS objects that cannot be consistently decoupled from gravity, a.k.a. supergravity strings. Following the completeness conjecture and requiring that their worldsheet theory is unitary imposes bounds on the admissible theories. We argue that for the anomaly-free six-dimensional theories it is more advantageous to study the unitarity constraints obtained after reduction to five dimensions. In general these are slightly more stringent and can be cast in a more geometric form, highly reminiscent of the Kodaira positivity condition (KPC). Indeed, for the F-theoretic models which have an underlying Calabi-Yau threefold these can be directly compared. The unitarity constraints (UC) are in general weaker than KPC, and maybe useful in understanding the consistent models without F-theoretic realisation. We catalogue the cases when UC is more restrictive than KPC, hinting at more refined hidden structure in elliptic Calabi-Yau threefolds with certain singularity structure.

From quantum link models to D-theory: a resource efficient framework for the quantum simulation and computation of gauge theories

Quantum link models provide an extension of Wilson’s lattice gauge theory in which the link Hilbert space is finite-dimensional and corresponds to a representation of an embedding algebra. In contrast to Wilson’s parallel transporters, quantum links are intrinsically quantum degrees of freedom. In D-theory, these discrete variables undergo dimensional reduction, thus giving rise to asymptotically free theories. In this way ( 1 + 1 ) -d C P ( N − 1 ) models emerge by dimensional reduction from ( 2 + 1 ) -d S U ( N ) quantum spin ladders, the ( 2 + 1 ) -d confining U ( 1 ) gauge theory emerges from the Abelian Coulomb phase of a ( 3 + 1 ) -d quantum link model, and ( 3 + 1 ) -d QCD arises from a non-Abelian Coulomb phase of a ( 4 + 1 ) -d S U ( 3 ) quantum link model, with chiral quarks arising naturally as domain wall fermions. Thanks to their finite-dimensional Hilbert space and their economical mechanism of reaching the continuum limit by dimensional reduction, quantum link models provide a resource efficient framework for the quantum simulation and computation of gauge theories. This article is part of the theme issue ‘Quantum technologies in particle physics’.

Using Sensorized Gloves and Dimensional Reduction for Hand Function Assessment of Patients with Osteoarthritis

Sensorized gloves allow the measurement of all hand kinematics that are essential for daily functionality. However, they are scarcely used by clinicians, mainly because of the difficulty of analyzing all joint angles simultaneously. This study aims to render this analysis easier in order to enable the applicability of the early detection of hand osteoarthritis (HOA) and the identification of indicators of dysfunction. Dimensional reduction was used to compare kinematics (16 angles) of HOA patients and healthy subjects while performing the tasks of the Sollerman hand function test (SHFT). Five synergies were identified by using principal component (PC) analyses, patients using less fingers arch, higher palm arching, and a more independent thumb abduction. The healthy PCs, explaining 70% of patients’ data variance, were used to transform the set of angles of both samples into five reduced variables (RVs): fingers arch, hand closure, thumb-index pinch, forced thumb opposition, and palmar arching. Significant differences between samples were identified in the ranges of movement of most of the RVs and in the median values of hand closure and thumb opposition. A discriminant function for the detection of HOA, based in RVs, is provided, with a success rate of detection higher than that of the SHFT. The temporal profiles of the RVs in two tasks were also compared, showing their potentiality as dysfunction indicators. Finally, reducing the number of sensors to only one sensor per synergy was explored through a linear regression, resulting in a mean error of 7.0°.

The visual arts

The visual arts, as compared to the performing arts, are defined by their static nature as fixed objects. However, visual art objects often have a ‘dual static/dynamic’ nature that allows them to convey a sense of both motion and emotion, especially when they depict human models. As a result, such objects appear to viewers as frozen snapshots of ongoing actions or gestures. The most art-specific process for the visual arts is the production of two-dimensional images. Compared with the production of three-dimensional objects, two-dimensional images require a dimensional reduction in order to create a flattened representation of a scene on a surface. Drawing is thus the ultimate visual arts activity.