The single-correlator conformal bootstrap is solved numerically for several values of dimension 4 > d > 2 using the available SDPB and Extremal Functional methods. Critical exponents and other conformal data of low-lying states are obtained over the entire range of dimensions with up to four-decimal precision and then compared with several existing results. The conformal dimensions of leading-twist fields are also determined up to high spin, and their d-dependence shows how the conformal states rearrange themselves around d = 2.2 for matching the Virasoro conformal blocks in the d = 2 limit. The decoupling of states at the Ising point is studied for 3 > d > 2 and the vanishing of one structure constant at d = 3 is found to persist till d = 2 where it corresponds to a Virasoro null-vector condition. arXiv:1811.07751v2 [hep-th]

We present a detailed microscopic study of edge excitations for n filled Landau levels. We show that the higher-level wavefunctions possess a non-trivial radial dependence that should be integrated over for properly defining the edge conformal field theory. This analysis let us clarify the role of the electron orbital spin s in the edge theory and to discuss its universality, thus providing a further instance of the bulk-boundary correspondence. We find that the values s i for each level, i = 1, . . . , n, parameterize a Casimir effect or chemical potential shift that could be experimentally observed. These results are generalized to fractional and hierarchical fillings by exploiting the W-infinity symmetry of incompressible Hall fluids.

This article presents the design and the experimental tests of a bioinspired robot mimicking the cownose ray. These fish swim by moving their large and flat pectoral fins, creating a wave that pushes backward the surrounding water so that the fish is propelled forward due to momentum conservation. The robot inspired by these animals has a rigid central body, housing motors, batteries, and electronics, and flexible pectoral fins made of silicone rubber. Each of them is actuated by a servomotor driving a link inside the leading edge, and the traveling wave is reproduced thanks to the flexibility of the fin itself. In addition to the pectoral fins, two small rigid caudal fins are present to improve the robot’s maneuverability. The robot has been designed, built, and tested underwater, and the experiments have shown that the locomotion principle is valid and that the robot is able to swim forward, perform left and right turns, and do floating or diving maneuvers.

The description of chiral quantum incompressible fluids by the W∞ symmetry can be extended from the edge, where it encompasses the conformal field theory approach, to the non-conformal bulk. The two regimes are characterized by excitations with different sizes, energies and momenta within the disk geometry. In particular, the bulk quantities have a finite limit for large droplets. We obtain analytic results for the radial shape of excitations, the edge reconstruction phenomenon and the energy spectrum of density fluctuations in Laughlin states.

This paper presents the design and construction of a biomimetic swimming robot inspired by the locomotion of rays. These fishes move by flapping their pectoral fins and creating a wave that moves in the opposite direction to the direction of motion, pushing the water back and giving the fish a propulsive force due to momentum conservation. While this motion is similar to other fishes in terms of efficiency, it gives better maneuverability and agility in turning. The robot's fins are molded from silicone rubber and moved by servo motors driving mechanisms inside the leading edge of each fin. The traveling wave, mimicking the movement of the fin, is passively generated by the flexibility of the material. The robot is also equipped with a tail that acts as a rudder, helpful in performing maneuvers and maintaining the desired attitude. The rigid central body of the robot is the housing for motors, electronics, and batteries. Sensors embedded in the robot allow to estimate its behavior, to compare different swimming strategies, and evaluate the best algorithm to control the robot.

Compact nonlocal Abelian gauge theory in (2 + 1) dimensions, also known as loop model, is a massless theory with a critical line that is explicitly covariant under duality transformations. It corresponds to the large N F limit of self-dual electrodynamics in mixed three-four dimensions. It also provides a bosonic description for surface excitations of three-dimensional topological insulators. Upon mapping the model to a local gauge theory in (3 + 1) dimensions, we compute the spectrum of electric and magnetic solitonic excitations and the partition function on the three torus T 3 . Analogous results for the S 2 × S 1 geometry show that the theory is conformal invariant and determine the manifestly self-dual spectrum of conformal fields, corresponding to order-disorder excitations with fractional statistics.

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