Spin Theory Research Articles

Quantum error correction and holographic information from bilocal holography

Bilocal holography is a constructive approach to the higher spin theory holographically dual to O(N ) vector models. In contrast to other approaches to bulk reconstruction, bilocal holography does not take input from the dual gravitational theory. The resulting map is a complete bulk/boundary mapping in that it maps the complete set of O(N ) invariant degrees of freedom in the CFT, to the complete set of higher spin degrees of freedom. After restricting to a suitable code subspace we demonstrate that bilocal holography naturally reproduces the quantum error correcting properties of holography and it gives a robust bulk (entanglement wedge) reconstruction. A gauge invariant entangled pair of CFT degrees of freedom are naturally smeared over a semicircle in the bulk spacetime, which is highly suggestive of bit threads. Finally, we argue that finite N relations in the CFT, when interpreted in the dual AdS spacetime, can provide relations between degrees of freedom located near the boundary and degrees of freedom deep in the bulk.

Theory of Spinors in Curved Space-Time

By means of Clifford Algebra, a unified language and tool to describe the rules of nature, this paper systematically discusses the dynamics and properties of spinor fields in curved space-time, such as the decomposition of the spinor connection, the classical approximation of the Dirac equation, the energy-momentum tensor of spinors and so on. To split the spinor connection into the Keller connection Υμ∈Λ1 and the pseudo-vector potential Ωμ∈Λ3 not only makes the calculation simpler, but also highlights their different physical meanings. The representation of the new spinor connection is dependent only on the metric, but not on the Dirac matrix. Only in the new form of connection can we clearly define the classical concepts for the spinor field and then derive its complete classical dynamics, that is, Newton’s second law of particles. To study the interaction between space-time and fermion, we need an explicit form of the energy-momentum tensor of spinor fields; however, the energy-momentum tensor is closely related to the tetrad, and the tetrad cannot be uniquely determined by the metric. This uncertainty increases the difficulty of deriving rigorous expression. In this paper, through a specific representation of tetrad, we derive the concrete energy-momentum tensor and its classical approximation. In the derivation of energy-momentum tensor, we obtain a spinor coefficient table Sabμν, which plays an important role in the interaction between spinor and gravity. From this paper we find that Clifford algebra has irreplaceable advantages in the study of geometry and physics.

Theory of spin–charge-coupled transport in proximitized graphene: an SO(5) algebraic approach

Establishing the conditions under which orbital, spin and lattice-pseudospin degrees of freedom are mutually coupled in realistic nonequilibrium conditions is a major goal in the emergent field of graphene spintronics. Here, we use linear-response theory to obtain a unified microscopic description of spin dynamics and coupled spin–charge transport in graphene with an interface-induced Bychkov–Rashba effect. Our method makes use of an SO(5) extension of the familiar inverse-diffuson approach to obtain a quantum kinetic equation for the single-particle density matrix that treats spin and pseudospin on equal footing and is valid for arbitrary external perturbations. As an application of the formalism, we derive a complete set of drift–diffusion equations for proximitized graphene with scalar impurities in the presence of electric and spin-injection fields which vary slowly in space and time. Our approach is amenable to a wide variety of generalizations, including the study of coupled spin–charge dynamics in layered materials with strong spin–valley coupling and spin–orbit torques in van der Waals heterostructures.

Spinning black hole binary dynamics, scattering amplitudes, and effective field theory

We describe a systematic framework for finding the conservative potential of compact binary systems with spin based on scattering amplitudes of particles of arbitrary spin and effective field theory. An arbitrary-spin formalism is generally required in the classical limit. By matching the tree and one-loop amplitudes of four spinning particles with those of a suitably chosen effective field theory, we obtain the ${\mathrm{spin}}_{1}\text{\ensuremath{-}}{\mathrm{spin}}_{2}$ terms of a two-body effective Hamiltonian through $\mathcal{O}({G}^{2})$ and valid to all orders in velocity. Solving Hamilton's equations yields the impulse and spin changes of the individual bodies. We write them in a surprisingly compact form as appropriate derivatives of the eikonal phase obtained from the amplitude. It seems likely this structure persists to higher orders. We also point out various double-copy relations for general spin.

Familial Spin: A Criminal Spin Theory Perspective on the Experiences of Parents and Siblings of Incarcerated Men

ABSTRACT The Criminal Spin theory focuses on a process, through which an individual experiences decreased feelings of self-control and empathy, along with increased criminal activity and self-centeredness. The different types of criminal spins (acute, chronic) and their levels (individual, group) are discussed in a familial context. This article focuses on the chronic group spin and its conceptual contribution to understanding the experiences of prisoners’ family members. A study of 27 members of prisoners’ nuclear families in Israel (i.e., parents and siblings) revealed that the imprisonment of a son or brother generates unique experiences that are similar to a group spin. An innovative angle to the theory referred to as the “familial spin” and its potential theoretical, social, and practical ramifications are discussed. Finally, positive criminology is suggested as a balanced approach that allows social acceptance and assists in preventing spin escalations and maintaining family members’ engagement with society and its values.

Actions for self-dual Higher Spin Gravities

Higher Spin Gravities are scarce, but covariant actions for them are even scarcer. We construct covariant actions for contractions of Chiral Higher Spin Gravity that represent higher spin extensions of self-dual Yang-Mills and self-dual Gravity theories. The actions give examples of complete higher spin theories both in flat and (anti)-de Sitter spaces that feature gauge and gravitational interactions. The actions are based on a new description of higher spin fields, whose origin can be traced to early works on twistor theory. The new description simplifies the structure of interactions. In particular, we find a covariant form of the minimal gravitational interaction for higher spin fields both in flat and anti-de Sitter space, which resolves some of the puzzles in the literature.

Spin and entanglement in general relativity

In a previous paper, we have shown how the classical and quantum relativistic dynamics of the Stueckelberg-Horwitz-Piron [SHP] theory can be embedded in general relativity (GR). We briefly review the SHP theory here and, in particular, the formulation of the theory of spin in the framework of relativistic quantum theory. We show here how the quantum theory of relativistic spin can be embedded, using a theorem of Abraham, Marsden and Ratiu, and also explicit derivation, into the framework of GR by constructing a local induced representation. The relation to the work of Fock and Ivanenko is also discussed. We show that in a gravitational field there is a highly complex structure for the spin distribution in the support of the wave function. We then discuss entanglement for the spins in a two body system.

Simulation and Theory of Classical Spin Hopping on a Lattice

The behavior of spin for incoherently hopping carriers is critical to understand in a variety of systems such as organic semiconductors, amorphous semiconductors, and muon-implanted materials. This work specifically examined the spin relaxation of hopping spin/charge carriers through a cubic lattice in the presence of varying degrees of energy disorder when the carrier spin is treated classically and random spin rotations are suffered during the hopping process (to mimic spin–orbit coupling effects) instead of during the wait time period (which would be more appropriate for hyperfine coupling). The problem was studied under a variety of different assumptions regarding the hopping rates and the random local fields. In some cases, analytic solutions for the spin relaxation rate were obtained. In all the models, we found that exponentially distributed energy disorder led to a drastic reduction in spin polarization losses that fell nonexponentially.

The dimensional reduction of linearized spin-2 theories invariant under transverse diffeomorphisms

Here we perform the Kaluza–Klein dimensional reduction from D+1 to D dimensions of massless Lagrangians described by a symmetric rank-2 tensor and invariant under transverse differmorphisms (TDiff). They include the linearized Einstein–Hilbert theory, linearized unimodular gravity and scalar tensor models. We obtain simple expressions in terms of gauge invariant field combinations and show that unitarity is preserved in all cases. After fixing a gauge, the reduced model becomes a massive scalar tensor theory. We show that the diffeomorphism (Diff) symmetry, instead of TDiff, is a general feature of the massless sector of consistent massive scalar tensor models. We discuss some subtleties when eliminating Stückelberg fields directly at action level as gauge conditions. A non local connection between the massless sector of the scalar tensor theory and the pure tensor TDiff model leads to a parametrization of the non conserved source which naturally separates spin-0 and spin-2 contributions in the pure tensor theory. The case of curved backgrounds is also investigated. If we truncate the non minimal couplings to linear terms in the curvature, vector and scalar constraints require Einstein spaces as in the Diff and WTDiff (Weyl plus Diff) cases. We prove that our linearized massive scalar tensor models admit those curved background extensions.

The Dirac Sea, T and C Symmetry Breaking, and the Spinor Vacuum of the Universe

We have developed a quantum field theory of spinors based on the algebra of canonical anticommutation relations (CAR algebra) of Grassmann densities in the momentum space. We have proven the existence of two spinor vacua. Operators C and T transform the normal vacuum into an alternative one, which leads to the breaking of the C and T symmetries. The CPT is the real structure operator; it preserves the normal vacuum. We have proven that, in the theory of the Dirac Sea, the formula for the charge conjugation operator must contain an additional generalized Dirac conjugation operator.

The 3d mathcal{N} = 6 bootstrap: from higher spins to strings to membranes

We study the space of 3d mathcal{N} = 6 SCFTs by combining numerical bootstrap techniques with exact results derived using supersymmetric localization. First we derive the superconformal block decomposition of the four-point function of the stress tensor multiplet superconformal primary. We then use supersymmetric localization results for the mathcal{N} = 6 U(N)k × U(N + M)−k Chern-Simons-matter theories to determine two protected OPE coefficients for many values of N, M, k. These two exact inputs are combined with the numerical bootstrap to compute precise rigorous islands for a wide range of N, k at M = 0, so that we can non-perturbatively interpolate between SCFTs with M-theory duals at small k and string theory duals at large k. We also present evidence that the localization results for the U(1)2M × U (1 + M)−2M theory, which has a vector-like large-M limit dual to higher spin theory, saturates the bootstrap bounds for certain protected CFT data. The extremal functional allows us to then conjecturally reconstruct low-lying CFT data for this theory.

Generalized elastic positivity bounds on interacting massive spin-2 theories

We use generalized elastic positivity bounds to constrain the parameter space of multi-field spin-2 effective field theories. These generalized bounds involve inelastic scattering amplitudes between particles with different masses, which contain kinematic singularities even in the t = 0 limit. We apply these bounds to the pseudo-linear spin-2 theory, the cycle spin-2 theory and the line spin-2 theory respectively. For the pseudo-linear theory, we exclude the remaining operators that are unconstrained by the usual elastic positivity bounds, thus excluding all the leading (or highest cutoff) interacting operators in the theory. For the cycle and line theory, our approach also provides new bounds on the Wilson coefficients previously unconstrained, bounding the parameter space in both theories to be a finite region (i.e., every Wilson coefficient being constrained from both sides). To help visualize these finite regions, we sample various cross sections of them and estimate the total volumes.

An improved parameter identification method of redundant manipulator

To achieve more accurate simulation and control in the use of the manipulator, it is necessary to establish an accurate dynamic model of the redundant manipulator. The research of this article focuses on the dynamic parameter identification method of the redundant manipulator. In the study, the spinor theory is applied to the Newton–Euler dynamic equation, the Coulomb + viscous friction model is adopted, and the minimum parameter set is obtained by linearization derivation. The parameter identification of the manipulator is realized using the method of offline identification of the measured current, and the coefficient of the excitation trajectory is optimized using the nonlinear optimization function. Finally, the parameter set with high accuracy is obtained, and the motion trajectory of each joint can be obtained. The scheme has high accuracy and can meet the needs of practical application. To verify the accuracy and reliability of this method, we have carried out experiments on a service robot “Walker” and obtained the desired results.

Non-destructive Testing Assisted by Six-Axis Manipulator Based on POE Formula

At present, aluminum plates are widely used in aerospace, machinery, and other fields because of their light weight, good manufacturability, and strong corrosion resistance. However, during long-term use, defects that will affect the structural strength such as cracks are easy to appear. Therefore, it is necessary to conduct automatic non-destructive testing of large metal plates to determine the location, size, and structural damage to their defects. Compared with manual detection, automated detection has many advantages such as high detection efficiency, high repeatability, strong flexibility, and low labor intensity. Based on the spinor theory, this paper uses the product of exponentials (POE) to model the kinematics of the Aubo-i5 manipulator and obtain the positive kinematics equations, which are compiled by analytic geometry and algebraic methods combined with Paden-Kahan subproblems and matrix theory. The inverse kinematics algorithm of the 6R manipulator is based on this model. An automated non-destructive testing system including a robotic arm and ultrasonic phased array testing equipment was built. At the same time, a robotic arm simulation platform was built based on ROS, and the inverse kinematics algorithm was used to control the robotic arm through the MoveIt!. The angle error can be controlled within 2.5°.

A method for assigning the motion precision of meta-action chain based on spinor theory

In order to provide theoretical guidance for the precision design and optimization of CNC machine tools, the motion precision distribution model of the meta-motion chain was established based on the minimum motion unit - meta-action. The motion function of CNC machine tool was decomposed into meta-action chain by using the “function-motion-action” (FMA) method, and the motion precision model of meta-action chain was established based on the screw theory. The sensitivity coefficient was used as the manufacturing cost index, and the spatial rotation error was used as the objective function to construct the motion precision distribution model. Finally, the NSGA-II genetic method was used to solve the distribution. The motion precision distribution of a numerical control machine tool is carried out, and the feasibility of the model is verified, which provides theoretical guidance for precision design of products.

The Grassmannian-like coset model and the higher spin currents

In the Grassmannian-like coset model, frac{mathrm{SU}{left(N+Mright)}_k}{mathrm{SU}{(N)}_ktimes mathrm{U}{(1)}_{kNMleft(N+Mright)}} , Creutzig and Hikida have found the charged spin-2, 3 currents and the neutral spin-2, 3 currents previously. In this paper, as an extension of Gaberdiel-Gopakumar conjecture found ten years ago, we calculate the operator product expansion (OPE) between the charged spin-2 current and itself, the OPE between the charged spin-2 current and the charged spin-3 current and the OPE between the neutral spin-3 current and itself for generic N, M and k. From the second OPE, we obtain the new charged quasi primary spin-4 current while from the last one, the new neutral primary spin-4 current is found implicitly. The infinity limit of k in the structure constants of the OPEs is described in the context of asymptotic symmetry of M×M matrix generalization of AdS3 higher spin theory. Moreover, the OPE between the charged spin-3 current and itself is determined for fixed (N, M) = (5, 4) with arbitrary k up to the third order pole. We also obtain the OPEs between charged spin-1, 2, 3 currents and neutral spin-3 current. From the last OPE, we realize that there exists the presence of the above charged quasi primary spin-4 current in the second order pole for fixed (N, M) = (5, 4). We comment on the complex free fermion realization.

Open 𝑟-Spin Theory I: Foundations

Abstract We lay the foundation for a version of $r$-spin theory in genus zero for Riemann surfaces with boundary. In particular, we define the notion of $r$-spin disks, their moduli space, and the Witten bundle; we show that the moduli space is a compact smooth orientable orbifold with corners, and we prove that the Witten bundle is canonically relatively oriented relative to the moduli space. In the sequel to this paper, we use these constructions to define open $r$-spin intersection theory and relate it to the Gelfand–Dickey hierarchy, thus providing an analog of Witten’s $r$-spin conjecture in the open setting.

Possible quadrupole order in tetragonal Ba2CdReO6 and chemical trend in the ground states of 5d 1 double perovskites

The synthesis and physical properties of the double perovskite (DP) compound Ba2CdReO6 with the 5d 1 electronic configuration are reported. Three successive phases originating from a spin–orbit-entangled J eff = 3/2 state, confirmed by a reduced effective magnetic moment of 0.72 μ B, were observed upon cooling. X-ray diffraction measurements revealed a structural transition from a high-temperature cubic structure to a low-temperature tetragonal structure at T s = 170 K, below which the J eff = 3/2 state was preserved. Magnetization, heat capacity, and thermal expansion measurements showed two more electronic transitions to a possible quadrupole ordered state at T q = 25 K and an antiferromagnetic order of dipoles with a ferromagnetic moment of ∼0.2 μ B at T m = 12 K. These properties were compared with those of the DP's sister compounds Ba2 BReO6 (B = Mg, Zn, and Ca) and the chemical trend is discussed in terms of the mean-field theory for spin–orbit-coupled 5d electrons (2010 Chen et al Phys. Rev. B 82 174440). The DP Ba2 BReO6 compounds provide a unique opportunity for a systematic investigation of symmetry breaking in the presence of multipolar degrees of freedom.

The mathcal{N} = 4 higher spin algebra for generic \u03bc parameter

The mathcal{N} = 4 higher spin generators for general superspin s in terms of oscillators in the matrix generalization of AdS3 Vasiliev higher spin theory at nonzero μ (which is equivalent to the ’t Hooft-like coupling constant λ) were found previously. In this paper, by computing the (anti)commutators between these mathcal{N} = 4 higher spin generators for low spins s1 and s2 (s1 + s2 ≤ 11) explicitly, we determine the complete mathcal{N} = 4 higher spin algebra for generic μ. The three kinds of structure constants contain the linear combination of two different generalized hypergeometric functions. These structure constants remain the same under the transformation μ ↔ (1 − μ) up to signs. We have checked that the above mathcal{N} = 4 higher spin algebra contains the mathcal{N} = 2 higher spin algebra, as a subalgebra, found by Fradkin and Linetsky some time ago.

Spectroscopic Expression of the External Surface Sites of H-ZSM-5

The nature and spectroscopic expression of external surface sites of zeolites, in particular ZSM-5, is a long-debated question. Herein, we use three cutting-edge techniques: Fourier-transform infrared spectroscopy (FTIR) with Fourier self-deconvolution (FSD), high magnetic field proton NMR spectroscopy under fast magic-angle spinning (MAS) and periodic boundary Density Functional Theory (DFT) calculations to study external surface models and analyze the effect of crystallite size. This provides an unequaled description of the various kinds of hydroxyl groups and of their proximities. The hydrogen-bond donor, acceptor or isolated nature of the hydroxyls results in distinct signals both in FTIR and NMR spectra, but the peak assignment is not the same from one technique to the other when the chemical nature of the hydroxyl changes. Bridging Si–(OH)–Al groups and Al–(H2O) lead to overlapping signals in one-dimensional 1H MAS NMR, whereas their contributions are strongly different in FTIR spectra. However, quantification and proximity assessment could only be obtained by 1H MAS NMR. With DFT, we confirm previous assignments for silanols and Si–(OH)–Al bridging OH groups. Other signals (between 3750 and 3600 cm–1, and between 1 and 4 ppm) are not only assigned to extra-framework species (which we confirm with dedicated models), but also enclose the signature of sites exposed at the external surface of ZSM-5. In particular, Al–(H2O) species (∼3665 cm–1; 3.8, 2.6 ppm) and silanol–Al (∼3740, 3720, 3665 cm–1; 2.6, 2.2 ppm) contribute to several features depending on their environment. μ1-Al–OH are also present at the external surface in low amount, with a 3780 cm–1 signal in IR, and weak signals in the 0–2 ppm interval in 1H MAS NMR.