Arbitrary Spin Research Articles

Constraints for twist-two alien operators in QCD

Parton evolution equations in QCD are controlled by the anomalous dimensions of gauge-invariant twist-two spin-N quark and gluon operators. Under renormalization, these mix with gauge-variant operators of the same quantum numbers, referred to as alien operators. Our work addresses the systematic study of these alien operators at arbitrary spin N, using generalized BRST symmetry relations to derive their couplings and Feynman rules at all values of N. We observe how the all-N structure of the generalized (anti-)BRST constraints relates the couplings of alien operators with n + 1 gluons to those with n gluons. Realizing a bootstrap, we present all one-loop results necessary for performing the operator renormalization up to four loops in QCD.

Quantum many-body scars for arbitrary integer spin in 2+1D Abelian gauge theories

The existence of quantum many-body scars, which prevents thermalization from certain initial states after a long time, has been established across different quantum many-body systems. These include gauge theories corresponding to spin-1/2 quantum link models. Establishing quantum scars in gauge theories with high spin is not accessible with existing numerical methods, which rely on exact diagonalization. We systematically identify scars for pure gauge theories with arbitrarily large integer spin S in 2+1D, where the electric field is restricted to 2S+1 states per link. Through an explicit analytic construction, we show that the presence of scars is widespread in 2+1D gauge theories for arbitrary integer spin. We confirm these findings numerically for small truncated spin and S=1 quantum link models. Our analytic construction establishes the presence of scars far beyond volumes and spins that can be probed with existing numerical methods and can guide quantum simulation experiments toward interesting nonequilibrium phenomena, inaccessible otherwise. Published by the American Physical Society 2024

Projective Spin Adaptation for the Exact Diagonalization of Isotropic Spin Clusters

Spin Hamiltonians, like the Heisenberg model, are used to describe the magnetic properties of exchange-coupled molecules and solids. For finite clusters, physical quantities, such as heat capacities, magnetic susceptibilities or neutron-scattering spectra, can be calculated based on energies and eigenstates obtained by exact diagonalization (ED). Utilizing spin-rotational symmetry SU(2) to factor the Hamiltonian with respect to total spin S facilitates ED, but the conventional approach to spin-adapting the basis is more intricate than selecting states with a given magnetic quantum number M (the spin z-component), as it relies on irreducible tensor-operator techniques and spin-coupling coefficients. Here, we present a simpler technique based on applying a spin projector to uncoupled basis states. As an alternative to Löwdin’s projection operator, we consider a group-theoretical formulation of the projector, which can be evaluated either exactly or approximately using an integration grid. An important aspect is the choice of uncoupled basis states. We present an extension of Löwdin’s theorem for s=12 to arbitrary local spin quantum numbers s, which allows for the direct selection of configurations that span a complete, linearly independent basis in an S sector upon the spin projection. We illustrate the procedure with a few examples.

[formula omitted] higher-spin supercurrents

We have constructed conserved N=2 higher-spin supercurrents for an arbitrary integer spin through the unconstrained superfield formulation of 4D,N=2 massless higher-spin theories in the harmonic superspace. The obtained supercurrents are gauge-invariant and determine consistent cubic interactions in the gauge superfield × supercurrent form for massless spin s1 and two massless spin s2N=2 supermultiplets. Such interactions and N=2 supercurrents exist only for s1≥2s2. These supercurrents are the N=2 supersymmetric extension of Berends-Burgers-van Dam higher-spin currents and generalize the linearized Bel-Robinson tensor. The relevant N=2 supercurrents can be considered as the descendants of the N=2 principle supercurrent, which has a simple universal structure. An important feature of our outcomes is that, ultimately, all N=2 supercurrents are built from the N=2 superfield strengths, which are constructed from the unconstrained analytical higher-spin prepotentials.

A foray on SCFT3 via super spinor-helicity and Grassmann twistor variables

In this paper, we develop a momentum super space formalism for N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1, 2 superconformal field theories in three dimensions. First, we solve for super-correlators in the usual momentum superspace variables. However, we found that expressing quantities in super space spinor helicity variables greatly simplifies the analysis. Further, by performing a “half” Fourier transform of the Grassmann coordinates which is analogous to the Twistor transform, an even more remarkable simplification occurs. Using this formalism, we first compute all three point correlation functions involving conserved super-currents with arbitrary spins in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1, 2 theories. We discover interesting double copy relations in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 super-correlators. Further, we discovered super double copy relations that take us from N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 to N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 super-correlators. We also extend our results to correlators involving scalars as well as to higher points. Further, we comment on the connection of our results with the flat space super amplitudes in one higher dimension.

Maxwell's equal area law for Vaidya-Bonner-de Sitter black hole under Lorentz invariance violation

In this study, we investigate the tunneling of fermions with arbitrary spin near the event horizon of a nonstationary Vaidya-Bonner-de Sitter (VBdS) black hole under Lorentz invariance violation (LIV). The modified Hawking temperature of VBdS black holes is calculated by using tortoise coordinate transformation, Feynman prescription, and Wentzel–Kramers–Brillouin approximation. By considering the cosmological constant as a thermodynamic pressure in the extended phase space, we construct a Maxwell's equal area law under LIV and study the phase transitions of VBdS black hole in , , and planes. The LIV increases the length of the liquid-gas coexistence region. The thermodynamic quantities such as the entropy, heat capacity, Helmholtz free energy, internal energy, enthalpy, and Gibbs free energy of the VBdS black hole are discussed. These quantities tend to increase under LIV. The stability of the black hole is also discussed in the presence of LIV.

Polarization analysis of two baryons with various spin combinations produced in electron-positron annihilation

We develop a systematic approach to analyze polarization correlations of two baryons B1B¯2 produced in the electron-positron annihilation process. With spin density matrices for arbitrary spin particles established in the standard, the Cartesian, and the helicity forms, we provide analyses of polarization correlations for two baryons with various spin combinations. This framework can be applied to determine the spin and the parity of excited baryons, and therefore offers opportunities for the investigation of baryon spectrum and transition form factors in present and future electron-positron annihilation experiments. Published by the American Physical Society 2024

Spinning binary dynamics in cubic effective field theories of gravity

We study the binary dynamics of two Kerr black holes with arbitrary spin vectors in the presence of parity-even and parity-odd cubic deformations of gravity. We first derive the tree-level Compton amplitudes for a Kerr black hole in cubic gravity, which we then use to compute the two-to-two amplitudes of the massive bodies to leading order in the deformation and the post-Minkowskian expansion. The required one-loop computations are performed using the leading singularity approach as well as the heavy-mass effective field theory (HEFT) approach. These amplitudes are then used to compute the leading-order momentum and spin kick in cubic gravity in the KMOC formalism. Our results are valid for generic masses and spin vectors, and include all the independent parity-even and parity-odd cubic deformations of Einstein-Hilbert gravity. We also present spin-expanded expressions for the momentum and spin kicks, and the all-order in spin deflection angle in the case of aligned spins.

On the equivalence between n-state spin and vertex models on the square lattice

In this paper we investigate a correspondence among spin and vertex models with the same number of local states on the square lattice with toroidal boundary conditions. We argue that the partition functions of an arbitrary n-state spin model and of a certain specific n-state vertex model coincide for finite lattice sizes. The equivalent vertex model has n3 non-null Boltzmann weights and their relationship with the edge weights of the spin model is explicitly presented. In particular, the Ising model in a magnetic field is mapped to an eight-vertex model whose weights configurations combine both even and odd number of incoming and outcoming arrows at a vertex. We have studied the Yang-Baxter algebra for such mixed eight-vertex model when the weights are invariant under arrows reversing. We find that while the Lax operator lie on the same elliptic curve of the even eight-vertex model the respective R-matrix can not be presented in terms of the difference of two rapidities. We also argue that the spin-vertex equivalence may be used to imbed an integrable spin model in the realm of the quantum inverse scattering framework. As an example, we show how to determine the R-matrix of the 27-vertex model equivalent to a three-state spin model devised by Fateev and Zamolodchikov.

A Relationship Between Spin and Geometry

In physics, spin is often seen exclusively through the lens of its phenomenological character: as an intrinsic form of angular momentum. However, there is mounting evidence that spin fundamentally originates as a quality of geometry, not of dynamics, and recent work further suggests that the structure of non-relativistic Euclidean three-space is sufficient to define it. In this paper, we directly explicate this fundamentally non-relativistic, geometric nature of spin by constructing non-commutative algebras of position operators which subsume the structure of an arbitrary spin system. These “Spin-s Position Algebras” are defined by elementary means and from the properties of Euclidean three-space alone, and constitute a fundamentally new model for quantum mechanical systems with non-zero spin, within which neither position and spin degrees of freedom, nor position degrees of freedom within themselves, commute. This reveals that the observables of a system with spin can be described completely geometrically as tensors of oriented planar elements, and that the presence of non-zero spin in a system naturally generates a non-commutative geometry within it. We will also discuss the potential for the Spin-s Position Algebras to form the foundation for a generalisation to arbitrary spin of the Clifford and Duffin–Kemmer–Petiau algebras.

Giant correlators at quantum level

We compute four-point functions with two maximal giant gravitons and two chiral primary operators at three-loop order in planar N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 Super-Yang-Mills theory. The Lagrangian insertion method, together with symmetries of the theory fix the integrand up to a few constants. Under the additional assumption of planarity, all these constants can be determined by lower loop data. The obtained result can be regarded as the planar diagram contribution to the full four-point function and is written in terms of the known three-loop conformal integrals. From the four-point function, we extract the OPE coefficients of two giant gravitons and one non-BPS twist-2 operator with arbitrary spin at three-loops, given in terms of harmonic sums. We observe an intriguingly simple relation between the giant graviton OPE coefficients and the OPE coefficients of three single-trace operators.

Triangular solutions to the reflection equation for Uq(sln^)

We study solutions of the reflection equation related to the quantum affine algebra Uq(sln^) . First, we explain how to construct a family of stochastic integrable vertex models with fixed boundary conditions. Then, we construct upper- and lower-triangular solutions of the reflection equation related to symmetric tensor representations of Uq(sln^) with arbitrary spin. We also prove the star–star relation for the Boltzmann weights of the Ising-type model, conjectured by Bazhanov and Sergeev, and use it to verify certain properties of the solutions obtained.

Deriving interaction vertices in higher derivative theories

We derive cubic interaction vertices for a class of higher-derivative theories involving three arbitrary integer spin fields. This derivation uses the requirement of closure of the Poincaré algebra in four-dimensional flat spacetime. We find two varieties of permitted structures at the cubic level and eliminate one variety, which is proportional to the equations of motion, using suitable field redefinitions. We then consider soft theorems for field theories with these higher-derivative interactions and construct amplitudes in these theories using the inverse-soft approach.

Kerr black hole shadows from axion-photon coupling

We have investigated the motion for photons in the Kerr black hole spacetime under the axion-photon coupling. The birefringence phenomena arising from the axion-photon coupling can be negligible in the weak coupling approximation because the leading-order contributions to the equations of motion come from the square term of the coupling parameter. We find that the coupling parameter makes the size of shadows slightly increase for arbitrary spin parameter. For the rapid rotating black hole case with a larger coupling, we find that there exist a “pedicel”-like structure appeared in the left of the “D”-type like shadows. Comparing the shadow size of the Kerr black hole with the shadow size of the Sgr A* and M87* black holes, we make constraints on the parameter space for such a theoretical model of the axion-photon coupling.

Optimal Spin Polarization Control for the Spin-Exchange Relaxation-Free System Using Adaptive Dynamic Programming.

This work is the first to solve the 3-D spin polarization control (3DSPC) problem of atomic ensembles, which controls the spin polarization to achieve arbitrary states with the cooperation of multiphysics fields. First, a novel adaptive dynamic programming (ADP) structure is proposed based on the developed multicritic multiaction neural network (MCMANN) structure with nonquadratic performance functions, as a way to solve the multiplayer nonzero-sum game (MP-NZSG) problem in 3DSPC under the constraints of asymmetric saturation inputs. Then, we utilize the MCMANNs to implement the multicritic multiaction ADP (MCMA-ADP) algorithm, whose convergence is proven by the compression mapping principle. Finally, the MCMA-ADP is deployed in the spin-exchange relaxation-free (SERF) system to provide a set of control laws in 3DSPC that fully exploits the multiphysics fields to achieve arbitrary spin polarization states. Numerical simulations support the theoretical results.

Higher categorical symmetries and gauging in two-dimensional spin systems

We present a framework to systematically investigate higher categorical symmetries in two-dimensional spin systems. Though exotic, such generalised symmetries have been shown to naturally arise as dual symmetries upon gauging invertible symmetries. Our framework relies on an approach to dualities whereby dual quantum lattice models only differ in a choice of module 2-category over some input fusion 2-category. Given an arbitrary two-dimensional spin system with an ordinary symmetry, we explain how to perform the (twisted) gauging of any of its sub-symmetries. We then demonstrate that the resulting model has a symmetry structure encoded into the Morita dual of the input fusion 2-category with respect to the corresponding module 2-category. We exemplify this approach by specialising to certain finite group generalisations of the transverse-field Ising model, for which we explicitly define lattice symmetry operators organised into fusion 2-categories of higher representations of higher groups.

Generic gravito-magnetic clock effects

ABSTRACT General relativity predicts that two counter-orbiting clocks around a spinning mass differ in the time required to complete the same orbit. The difference in these two values for the orbital period is generally referred to as the gravito-magnetic (GM) clock effect. It has been proposed to measure the GM clock effect using atomic clocks carried by satellites in prograde and retrograde orbits around the Earth. The precision and stability required for satellites to accurately perform this measurement remains a challenge for current instrumentation. One of the most accurate clocks in the Universe is a millisecond pulsar, which emits periodic radio pulses with high stability. Timing of the pulsed signals from millisecond pulsars has proven to be very successful in testing predictions of general relativity and the GM clock effect is potentially measurable in binary systems. In this work, we derive the generic GM clock effect by considering a slowly spinning binary system on an elliptical orbit, with both arbitrary mass ratio and arbitrary spin orientations. The spin–orbit interaction introduces a perturbation to the orbit, causing the orbital plane to precess and nutate. We identify several different contributions to the clock effects: the choice of spin supplementary condition and the observer-dependent definition of a full revolution and ‘nearly identical’ orbits. We discuss the impact of these subtle definitions on the formula for GM clock effects and show that most of the existing formulae in the literature can be recovered under appropriate assumptions.

Universal determination of comagnetometer response to spin couplings

We propose and demonstrate a general method to calibrate the frequency-dependent response of self-compensating noble-gas–alkali-metal comagnetometers to arbitrary spin perturbations. This includes magnetic and nonmagnetic perturbations such as rotations and exotic spin interactions. The method is based on a fit of the magnetic field response to an analytical model. The frequency-dependent response of the comagnetometer to arbitrary spin perturbations can be inferred using the fit parameters. We demonstrate the effectiveness of this method by comparing the inferred rotation response to an experimental measurement of the rotation response. Our results show that experiments relying on zero-frequency calibration of the comagnetometer response can over- or underestimate the comagnetometer sensitivity by orders of magnitude over a wide frequency range. Moreover, this discrepancy accumulates over time as operational parameters tend to drift during comagnetometer operation. The demonstrated calibration protocol enables accurate prediction and control of comagnetometer sensitivity to, for example, ultralight bosonic dark-matter fields coupling to electron or nuclear spins, as well as accurate monitoring and control of the relevant system parameters. Published by the American Physical Society 2024

On correlation functions of higher-spin currents in arbitrary dimensions d > 3

We revisit the problem of classification and explicit construction of the conformal three-point correlation functions of currents of arbitrary integer spin in arbitrary dimensions. For the conserved currents, we set up the equations for the conservation conditions and solve them completely for some values of spins, confirming the earlier counting of the number of independent structures matching them with the higher-spin cubic vertices in one higher dimension. The general solution for the correlators of conserved currents we delegate to a follow-up work.

New physical insights into the supporting subspace factorization of XMS-CASPT2 and generalization to multiple spin states via spin-free formulation.

This paper introduces a spin-free formulation of the supporting subspace factorization [C. Song and T. J. Martínez, J. Chem. Phys. 149, 044108 (2018)], enabling a reduction in the computational scaling of the extended multi-state complete active space second-order perturbation (XMS-CASPT2) method for arbitrary spins. Compared to the original formulation that is defined in the spin orbitals and is limited to singlet states, the spin-free formulation in this work treats different spin states equivalently, thus naturally generalizing the idea beyond singlet states. In addition, we will present a new way of deriving the supporting subspace factorization with the purpose of understanding its physical interpretation. In this new derivation, we separate the sources that make CASPT2 difficult into the "same-site interactions" and "inter-site interactions." We will first show how the Kronecker sum can be used to remove the same-site interactions in the absence of inter-site interactions, leading to MP2 energy in dressed orbitals. We will then show how the inter-site interactions can be exactly recovered using Löwdin partition, where the supporting subspace concept will naturally arise. The new spin-free formulation maintains the main advantage of the supporting subspace factorization, i.e., allowing XMS-CASPT2 energies to be computed using highly optimized MP2 energy codes and Fock build codes, thus reducing the scaling of XMS-CASPT2 to the same scaling as MP2. We will present and discuss results that benchmark the accuracy and performance of the new method. To demonstrate how the new method can be useful in studying real photochemical systems, the supporting subspace XMS-CASPT2 is applied to a photoreaction sensitive to magnetic field effects. The new spin-free formulation makes it possible to calculate the doublet and quartet states required in this particular photoreaction mechanism.