Asymptotic symmetries in Carrollian theories of gravity

Asymptotic symmetries in Carrollian gravitational theories in 3+1 space and time dimensions obtained from “magnetic” and “electric” ultrarelativistic contractions of General Relativity are analyzed. In both cases, parity conditions are needed to guarantee a finite symplectic term, in analogy with Einstein gravity. For the magnetic contraction, when Regge-Teitelboim parity conditions are imposed, the asymptotic symmetries are described by the Carroll group. With Henneaux-Troessaert parity conditions, the asymptotic symmetry algebra corresponds to a BMS-like extension of the Carroll algebra. For the electric contraction, because the lapse function does not appear in the boundary term needed to ensure a well-defined action principle, the asymptotic symmetry algebra is truncated, for Regge-Teitelboim parity conditions, to the semidirect sum of spatial rotations and spatial translations. Similarly, with Henneaux-Troessaert parity conditions, the asymptotic symmetries are given by the semidirect sum of spatial rotations and an infinite number of parity odd supertranslations. Thus, from the point of view of the asymptotic symmetries, the magnetic contraction can be seen as a smooth limit of General Relativity, in contrast to its electric counterpart.

Linearized supergravity with a dynamical preferred frame

We study supersymmetric extension of the Einstein-aether gravitational model where local Lorentz invariance is broken down to the subgroup of spatial rotations by a vacuum expectation value of a timelike vector field called aether. Embedding aether into a chiral vector superfield, we construct the most general action which describes dynamics of linear perturbations around the Lorentz-violating vacuum and is invariant under the linearized supergravity transformations. The analysis is performed both in the off-shell non-minimal superfield formulation of supergravity and in the “on-shell” approach invoking only physical component fields. The resulting model contains a single free coupling, in addition to the standard supergravity parameters. The spectrum of physical excitations features an enhanced on-shell gravity multiplet comprising four states with helicities 2, 3/2, 3/2 and 1 propagating with superluminal velocity. The remaining excitations propagate with the speed of light. We outline the observational constraints on the model following from its low-energy phenomenology.

Intuitive Physical Human-Robot Interaction using an Underactuated Redundant Manipulator with Complete Spatial Rotational Capabilities

In this paper, the concept of underactuated redundancy is presented using a novel spatial two-degree-of-freedom (2-DoF) gravity balanced rotational manipulator, composed of movable counterweights. The proposed kinematic arrangement makes it possible to intuitively manipulate a payload undergoing 3-DoF spatial rotations by adding a third rotational axis oriented in the direction of gravity. The static equilibrium equations of the 2-DoF architecture are first described in order to provide the required configuration of the counterweights for a statically balanced mechanism. A method for calibrating the mechanism, which establishes the coefficients of the static equilibrium equations, is also presented. In order to both translate and rotate the payload during manipulation, the rotational manipulator is mounted on an existing translational manipulator. Experimental validations of both systems are presented to demonstrate the intuitive and responsive behaviour of the manipulators during physical human-robot interactions.

Electromagnetic duality and D3-brane scattering amplitudes beyond leading order

We use on-shell methods to study the non-supersymmetric and supersymmetric low-energy S-matrix on a probe D3-brane, including both the 1-loop contributions of massless states as well as the effects of higher-derivative operators. Our results include: (1) A derivation of the duality invariance of Born-Infeld electrodynamics as the dimensional oxidation of the group of spatial rotations transverse to a probe M2-brane; this is done using a novel implementation of subtracted on-shell recursion. (2) The first explicit loop-level BCJ double-copy in a non-gravitational model, namely the calculation of the 4-point self-dual amplitude of non-supersymmetric Born-Infeld. (3) From previous results for n-point self-dual 1-loop BI amplitudes and the conjectured dimension-shifting relations in Yang-Mills, we obtain an explicit all-multiplicity, at all orders in E, expression for the 1-loop integrand of the MHV sector of $$ \mathcal{N} $$ N = 4 DBI. (4) For all n > 4, the explicitly integrated duality-violating 1-loop amplitudes (self-dual and next-to-self-dual in pure BI as well as MHV in $$ \mathcal{N} $$ N = 4 DBI) are shown to be removable at $$ \mathcal{O}\left({\upepsilon}^0\right) $$ O ϵ 0 by adding finite local counterterms; we propose that this may be true more generally at 1-loop order. (5) We find that in non-supersymmetric Born-Infeld, not all finite local counterterms needed to restore electromagnetic duality can be constructed using the double-copy with higher-derivative corrections, suggesting a fundamental tension between electromagnetic duality and color-kinematics duality at loop-level. Finally we comment on oxidation of duality symmetries in supergravity and the parallels it has to the M2-brane to D3-brane oxidation demonstrated in this paper.

Exceptional nonrelativistic effective field theories with enhanced symmetries

We initiate the classification of nonrelativistic effective field theories (EFTs) for Nambu-Goldstone (NG) bosons, possessing a set of redundant, coordinate-dependent symmetries. Similarly to the relativistic case, such EFTs are natural candidates for “exceptional” theories, whose scattering amplitudes feature an enhanced soft limit, that is, scale with a higher power of momentum at long wavelengths than expected based on the mere presence of Adler’s zero. The starting point of our framework is the assumption of invariance under spacetime translations and spatial rotations. The setup is nevertheless general enough to accommodate a variety of nontrivial kinematical algebras, including the Poincaré, Galilei (or Bargmann) and Carroll algebras. Our main result is an explicit construction of the nonrelativistic versions of two infinite classes of exceptional theories: the multi-Galileon and the multi-flavor Dirac-Born-Infeld (DBI) theories. In both cases, we uncover novel Wess-Zumino terms, not present in their relativistic counterparts, realizing nontrivially the shift symmetries acting on the NG fields. We demonstrate how the symmetries of the Galileon and DBI theories can be made compatible with a nonrelativistic, quadratic dispersion relation of (some of) the NG modes.

Statistics of spatial rotations and projection directions considering molecular symmetry in 3D electron cryo-microscopy

Electron cryo-microscopy (cryoEM) three-dimensional (3D) reconstruction is based on estimations of orientations of projection images or 3D volumes. It is common that the macromolecules studied by cryoEM have molecular symmetry, which, unfortunately, has not been taken into consideration by any statistics for either spatial rotations or projection directions at this point. Meanwhile, there are growing needs to adopt advanced statistical methods, and further, modern machine learning techniques in cryoEM. Since those methodologies are built heavily upon statistical learning cornerstones, the absence of their domain-specific statistical justification limits their applications in cryoEM. In this research, based on the concept of non-unique-games (NUG), we propose two key statistical measurements, the mean and the variance, of both spatial rotations and projection directions when molecular symmetry is considered. Such methods are implemented in the open-source python package pySymStat.

Statistics of spatial rotations in 3D electron cryo-microscopy by unit quaternion description

Electron cryo-microscopy (cryoEM) involves the estimation of orientations of projection images or three-dimensional (3D) volumes. However, the lack of statistical tools of rotations in cryoEM fails to answer the growing demands for adopting advanced statistical methods. In this study, we develop a comprehensive statistical tool specialized for cryoEM based on an unit quaternion description of spatial rotations. Some basic properties and definitions of the quaternion, as well as a way to use the unit quaternion to describe and perform rotations, are first recalled. Then, based on the unit quaternion, the distance and geodesic between rotations are designed for cryoEM to enable comparisons and interpolations between rotations, which are prerequisites of statistics of rotations in 3D cryoEM. Further, methods of directional statistics specialized for cryoEM are developed, including calculations of the average rotation, sampling, and inference with uniform and angular central Gaussian (ACG) distribution, as well as an estimation of the rotation precision. Finally, the method of handling molecular symmetry is introduced. Using the unit quaternion system for cryoEM, we provide comprehensive mathematical tools for the analysis of spatial rotations in cryoEM.