Extra Symmetry Research Articles

Regularizable collinear periodic solutions in the n-body problem with arbitrary masses

For n-body problem with arbitrary positive masses, we prove there are regularizable collinear periodic solutions for any ordering of the masses, going from a simultaneous binary collision to another in half of a period with half of the masses moving monotonically to the right and the other half monotonically to the left. When the masses satisfy certain equality condition, the solutions have extra symmetry. This also gives a new proof of the existence of Schubart orbit, when n=3.

Insulating behaviour in room temperature rhombohedral LiNiO2 cathodes is driven by dynamic correlation

Abstract Inspired by the experimental finding of a paramagnetic insulating state in rhombohedral LiNiO2, a lithium-ion battery cathode of great interest, we calculate the electronic, magnetic, and optical properties of LiNiO2 employing a range of single-particle and many-body methods. Within density-functional theory (DFT) using the generalized-gradient approximation (GGA), meta-GGA, and hybrid functionals, we obtain a ferromagnetic half-metallic ground state for rhombohedral LiNiO2, as has been seen previously. Self-consistent GW calculations including self-interaction corrections beyond DFT for various flavours show an electronic band gap albeit with a small quasiparticle peak at the Fermi energy. Moving beyond this, room temperature state-of-the-art dynamical mean-field theory (DMFT) calculations on rhombohedral LiNiO2 show for the first time a gap of combined Mott and charge-transfer character. The paramagnetic insulating state has a band gap of ~0.6 eV, in excellent agreement with experiments and is in sharp contrast to DFT calculations that require the presence of an extra structural symmetry breaking in the form of Jahn–Teller distortions to open a gap. We observe Ni to be in a +2 state in a d 8L configuration, with a charge-transfer ligand hole in O p, and identify the ligand hole state from the DMFT DOS. We further show that whereas DFT shows the presence of an unphysical metallic Drude peak in the optical absorption spectra, DMFT calculations capture the correct form of the optical absorption spectra, and have an excellent match with the calculated band gap as well. Our results clarify that at room temperature, it is the charge transfer gap with a Mott character that causes rhombohedral LiNiO2’s insulating nature; a structural distortion is not required.

Quantum backreactions in (A)dS3 massive gravity and logarithmic asymptotic behavior

We study the interplay between higher-curvature terms and the backreaction of quantum fluctuations in three-dimensional massive gravity in asymptotically (anti–)de Sitter space. We focus on the theory at the special point of the parameter space where the two maximally symmetric vacua coincide. In the case of positive cosmological constant, this corresponds to the partially massless point, at which the classical theory admits de Sitter black holes and exhibits an extra conformal symmetry at linear level. We explicitly find the quantum corrected black hole geometry in the semiclassical approximation and show that it induces a relaxation of the standard asymptotic conditions. Nonetheless, the new asymptotic behavior is still preserved by an infinite-dimensional algebra, which, in addition to Virasoro, contains logarithmic supertranslations. Finally, we show that all the results we obtain for the quadratic massive gravity theory can be extended to theories including cubic and quartic terms in the curvature. Published by the American Physical Society 2024

Classifying large N limits of multiscalar theories by algebra

We develop a new approach to RG flows and show that one-loop flows in multiscalar theories can be described by commutative but non-associative algebras. As an example related to D-brane field theories and tensor models, we study the algebra of a theory with M SU(N) adjoint scalars and its large N limits. The algebraic concepts of idempotents and Peirce numbers/Kowalevski exponents are used to characterise the RG flows. We classify and describe all large N limits of algebras of multiadjoint scalar models: the standard ‘t Hooft matrix theory limit, a ‘multi-matrix’ limit, each with one free parameter, and an intermediate case with extra symmetry and no free parameter of the algebra, but an emergent free parameter from a line of one-loop fixed points. The algebra identifies these limits without diagrammatic or combinatorial analysis.

Scalar sector interactions in BDW model

In the Bélanger-Delaunay-Westhoff model, vectorlike fermions and a new scalar sector charged under an extra Abelian gauge symmetry are introduced to explain the flavor observables, and the muon . In this paper, we focus our study to the scalar sector of this model and the relevant interactions. The interaction terms including the exotic Yukawa, the gauge interactions, and the scalar 3-point and 4-point interactions are derived together with the corresponding Feynman rules. It is shown that the new scalar can decay into a pair of standard-model-like Higgs bosons. This channel is considered by analyzing the decay width and its parameter dependence.

The partial Bondi gauge: Gauge fixings and asymptotic charges

In the companion paper [SciPost Phys. 13, 108 (2022)] we have studied the solution space at null infinity for gravity in the partial Bondi gauge. This partial gauge enables to recover as particular cases and among other choices the Bondi-Sachs and Newman-Unti gauges, and to approach the question of the most general boundary conditions and asymptotic charges in gravity. Here we compute and study the asymptotic charges and their algebra in this partial Bondi gauge, by focusing on the flat case with a varying boundary metric \delta q_{AB}≠0δqAB≠0. In addition to the super-translations, super-rotations, and Weyl transformations, we find two extra asymptotic symmetries associated with non-vanishing charges labelled by free functions in the solution space. These new symmetries arise from a weaker definition of the radial coordinate and switch on traces in the transverse metric. We also exhibit complete gauge fixing conditions in which these extra asymptotic symmetries and charges survive. As a byproduct of this calculation we obtain the charges in Newman-Unti gauge, in which one of these extra asymptotic charges is already non-vanishing. We also apply the formula for the charges in the partial Bondi gauge to the computation of the charges for the Kerr spacetime in Bondi coordinates.

Democratic Lagrangians from topological bulk

Chiral form fields in d dimensions can be effectively described as edge modes of topological Chern-Simons theories in d+1 dimensions. At the same time, manifestly Lorentz-invariant Lagrangian description of such fields directly in terms of a d-dimensional field theory is challenging and requires introducing nontrivial auxiliary gauge fields eliminated on shell with extra gauge symmetries. A recent work by Arvanitakis demonstrates (emphasizing the case of 2d chiral bosons) that the two approaches are related, and a peculiar reduction on the (d+1)-dimensional topological Lagrangian automatically leads to d-dimensional Lagrangians with appropriate sets of auxiliary fields. We develop this setup in three distinct directions. First, we demonstrate how arbitrary Abelian self-interactions for chiral forms can be included using nonlinear boundary terms in the Chern-Simons theory. Second, by generalizing the Chern-Simons theory to the BF-theory, we obtain an analogous democratic description of nonchiral form fields, where electric and magnetic potentials appear as explicit dynamical variables. Third, we discuss the effects of introducing topological interactions in the higher-dimensional bulk, which produce extra interaction terms in the boundary theory. When applied to a topological 4-form field in 12 dimensions, this construction results in a democratic description of the 3-form gauge field of the eleven-dimensional supergravity. Published by the American Physical Society 2024

Neutrino charge radius and electromagnetic dipole moments via scalar and vector leptoquarks

The one-loop contribution of scalar and vector leptoquarks (LQs) to the electromagnetic properties (NEPs) of massive Dirac neutrinos is presented via an effective Lagrangian approach. For the contribution of gauge LQs to the effective neutrino charge radius defined in Bernabeu et al. (Phys Rev Lett 89:101802, 2002. https://doi.org/10.1103/PhysRevLett.89.101802 [Erratum: Phys Rev Lett 89:229902 (2002)]), we considered a Yang–Mills scenario and used the background field method for the calculation. Analytical results for nonzero neutrino mass are presented, which can be useful to obtain the NEPs of heavy neutrinos, out of which approximate expressions are obtained for light neutrinos. For the numerical analysis we concentrate on the only renormalizable scalar and vector LQ representations that do not need extra symmetries to forbid tree-level proton decay. Constraints on the parameter space consistent with current experimental data are then discussed and it is found that the scalar R~2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\widetilde{R}}_2$$\\end{document} and the vector U1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$U_1$$\\end{document} representations could yield the largest LQ contributions to the NEPs: for LQ couplings to both left- and right handed neutrinos of the order of O(1) and a LQ mass of 1.5-2 TeV, the magnetic dipole moment (MDM) of a Dirac neutrino with a mass in the eV scale can be of the order of 10-9\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-9}$$\\end{document}–10-10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-10}$$\\end{document}μB\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu _B$$\\end{document}, whereas its neutrino electric dipole moment (EDM) can reach values as high as 10-20\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-20}$$\\end{document}–10-19\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-19}$$\\end{document} ecm. On the other hand, the effective NCR can reach values up to 10-35\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-35}$$\\end{document} cm2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^2$$\\end{document} even if LQs do not couple to right-handed neutrinos, in which case the EDM vanishes and the contribution to the MDM would be negligible.

Quantization of Weyl invariant unimodular gravity with antisymmetric ghost fields

The enforcement of the unimodularity condition in a gravity theory by means of a Lagrange multiplier leads, in general, to inconsistencies upon quantization. This is so, in particular, when the classic linear splitting of the metric between the background and quantum fields is used. To avoid the need of introducing such a Lagrange multiplier while using the classic linear splitting, we carry out the quantization of unimodular gravity with extra Weyl symmetry by using Becchi–Rouet–Stora–Tyutin (BRST) techniques. Here, two gauge symmetries are to be gauge-fixed: transverse diffeomorphisms and Weyl transformations. We perform the gauge-fixing of the transverse diffeomorphism invariance by using BRST transformations that involve antisymmetric ghost fields. We show that these BRST transformations are compatible with the BRST transformations needed to gauge-fix the Weyl symmetry, so that they can be combined in a set of transformations generated by a single BRST operator. Newton’s law of gravitation is derived within the BRST formalism we put forward as well as the Slavnov–Taylor equation.

Quantum graphs: Different perspectives, homomorphisms and quantum automorphisms

We undertake a study of the notion of a quantum graph over arbitrary finite-dimensional C ∗ C^* -algebras B B equipped with arbitrary faithful states. Quantum graphs are realised principally as either certain operators on L 2 ( B ) L^2(B) , the quantum adjacency matrices, or as certain operator bimodules over B ′ B’ . We present a simple, purely algebraic approach to proving equivalence between these settings, thus recovering existing results in the tracial state setting. For non-tracial states, our approach naturally suggests a generalisation of the operator bimodule definition, which takes account of (some aspect of) the modular automorphism group of the state. Furthermore, we show that each such “non-tracial” quantum graph corresponds to a “tracial” quantum graph which satisfies an extra symmetry condition. We study homomorphisms (or CP-morphisms) of quantum graphs arising from unital completely positive (UCP) maps, and the closely related examples of quantum graphs constructed from UCP maps. We show that these constructions satisfy automatic bimodule properties. We study quantum automorphisms of quantum graphs, give a definition of what it means for a compact quantum group to act on an operator bimodule, and prove an equivalence between this definition, and the usual notion defined using a quantum adjacency matrix. We strive to give a relatively self-contained, elementary, account, in the hope this will be of use to other researchers in the field.

On the Arithmetic of Generalized Fekete Polynomials

For each prime number p one can associate a Fekete polynomial with coefficients–1 or 1 except the constant term, which is 0. These are classical polynomials that have been studied extensively in the framework of analytic number theory. In a recent paper, we showed that these polynomials also encode interesting arithmetic information. In this article, we define generalized Fekete polynomials associated with quadratic characters whose conductors could be composite numbers. We then investigate the appearance of cyclotomic factors in these generalized Fekete polynomials. Based on this investigation, we introduce a compact version of Fekete polynomials as well as their trace polynomials. We then study the Galois groups of these Fekete polynomials using modular techniques. In particular, we discover some surprising extra symmetries which imply some restrictions on the corresponding Galois groups. Finally, based on both theoretical and numerical data, we propose a precise conjecture on the structure of these Galois groups.

Baryogenesis in a parity solution to the strong CP problem

Space-time parity can solve the strong CP problem and introduces a spontaneously broken SU(2)R gauge symmetry. We investigate the possibility of baryogenesis from a first-order SU(2)R phase transition similar to electroweak baryogenesis. We consider a model with the minimal Higgs content, for which the strong CP problem is indeed solved without introducing extra symmetry beyond parity. Although the parity symmetry seems to forbid the SU(2)R anomaly of the B − L symmetry, the structure of the fermion masses can allow for the SU(2)R sphaleron process to produce non-zero B − L asymmetry of Standard Model particles so that the wash out by the SU(2)L sphaleron process is avoided. The setup predicts a new hyper-charged fermion whose mass is correlated with the SU(2)R symmetry breaking scale and hence with the SU(2)R gauge boson mass, and depending on the origin of CP violation, with an electron electric dipole moment. In a setup where CP violation and the first-order phase transition are assisted by a singlet scalar field, the singlet can be searched for at future colliders.

U(1) L μ -L τ breaking phase transition, muon g–2, dark matter, collider, and gravitational wave* *Supported by the National Natural Science Foundation of China (11975013), and the the Natural Science Foundation of Shandong Province, China (ZR2023MA038)

Combining the dark matter and muon anomaly, we study the breaking phase transition, gravitational wave spectra, and direct detection at the LHC in an extra gauge symmetry extension of the standard model. The new fields include vector-like leptons ( ), the breaking scalar S, and the gauge boson , as well as the dark matter candidate and its heavy partner . A joint explanation of the dark matter relic density and muon anomaly excludes the region where both and are much larger than . In the parameter space accommodating the DM relic density and muon anomaly, the model can achieve a first-order breaking phase transition, whose strength is sensitive to the parameters of the Higgs potential. The corresponding gravitational wave spectra can reach the sensitivity of U-DECIGO. In addition, the direct searches at the LHC impose stringent bounds on the mass spectra of the vector-like leptons and dark matter.

Many versus one: The disorder operator and entanglement entropy in fermionic quantum matter

Motivated by recent development of the concept of the disorder operator and its relation with entanglement entropy in bosonic systems, here we show the disorder operator successfully probes many aspects of quantum entanglement in fermionic many-body systems. From both analytical and numerical computations in free and interacting fermion systems in 1D and 2D, we find the disorder operator and the entanglement entropy exhibit similar universal scaling behavior, as a function of the boundary length of the subsystem, but with subtle yet important differences. In 1D they both follow the \log{L}logL scaling behavior with the coefficient determined by the Luttinger parameter for disorder operator, and the conformal central charge for entanglement entropy. In 2D they both show the universal L\log LLlogL scaling behavior in free and interacting Fermi liquid states, with the coefficients depending on the geometry of the Fermi surfaces. However at a 2D quantum critical point with non-Fermi-liquid state, extra symmetry information is needed in the design of the disorder operator, so as to reveal the critical fluctuations as does the entanglement entropy. Our results demonstrate the fermion disorder operator can be used to probe quantum many-body entanglement related to global symmetry, and provide new tools to explore the still largely unknown territory of highly entangled fermion quantum matter in 2 or higher dimensions.

Net Dzyaloshinskii–Moriya interaction in defect-enriched ferromagnet

The Dzyaloshinskii–Moriya interaction (DMI), which typically occurs in lattices without space inversion symmetry, can also be induced in a highly symmetric lattice by local symmetry breaking due to any lattice defect. We recently presented an experimental study of polarized small angle neutron scattering (SANS) on the nanocrystalline soft magnet Vitroperm (Fe73Si16B7Nb3Cu1), where the interface between the FeSi nanoparticles and the amorphous magnetic matrix serves as such a defect. The SANS cross sections exhibited the polarization-dependent asymmetric term originating from the DMI. One would naturally expect the defects characterized by a positive and a negative DMI constant D to be randomly distributed and this DMI-induced asymmetry to disappear. Thus, the observation of such an asymmetry indicates that there exists an extra symmetry breaking. In the present work we experimentally explore the possible causes by measuring the DMI-induced asymmetry in the SANS cross sections of the Vitroperm sample tilted in different directions with respect to the external magnetic field. Furthermore, we analyzed the scattered neutron beam using a spin filter based on polarized protons and confirm that the asymmetric DMI signal originates from the difference between the two spin-flip scattering cross-sections.

Nonperturbative regularization of ( 1+1 )-dimensional anomaly-free chiral fermions and bosons: On the equivalence of anomaly matching conditions and boundary gapping rules

A non-perturbative lattice regularization of chiral fermions and bosons with anomaly-free symmetry $G$ in 1+1D spacetime is proposed. More precisely, we ask "whether there is a local short-range quantum Hamiltonian with a finite Hilbert space for a finite system realizing onsite symmetry $G$ defined on a 1D spatial lattice, such that its low energy physics produces a 1+1D anomaly-free chiral matter theory of symmetry $G$?" In particular, we propose that the 3$_L$-5$_R$-4$_L$-0$_R$ U(1) chiral fermion theory, with two left-moving fermions of charge-3 and 4, and two right-moving fermions of charge-5 and 0 at low energy, can be put on a 1D spatial lattice where the U(1) symmetry is realized as an onsite symmetry, if we include properly designed multi-fermion interactions with intermediate strength. In general, we propose that any 1+1D U(1)-anomaly-free chiral matter theory can be defined as a finite system on a 1D lattice with onsite symmetry by using a quantum Hamiltonian with continuous time, but without suffering from Nielsen-Ninomiya theorem's fermion-doubling, if we include properly-designed interactions between matter fields. We propose how to design such interactions by looking for extra symmetries via bosonization/fermionization. We comment on the new ingredients and the differences of ours compared to Ginsparg-Wilson fermion, Eichten-Preskill, and Chen-Giedt-Poppitz (CGP) models, and suggest modifying CGP model to have successful mirror-decoupling. We show a topological non-perturbative proof of the equivalence between $G$-symmetric 't Hooft anomaly cancellation conditions and $G$-symmetric gapping rules (e.g. Haldane's stability conditions for Luttinger liquid) for multi-U(1) symmetry. We expect our result holds universally regardless of spatial Hamiltonian or Lagrangian/spacetime path integral formulation. Numerical tests are demanding tasks but highly desirable for future work.

Entropy bounds, compactness and finiteness theorems for embedded self-shrinkers with rotational symmetry

Abstract In this work, we study the space of complete embedded rotationally symmetric self-shrinking hypersurfaces in ℝ n + 1 {\mathbb{R}^{n+1}} . First, using comparison geometry in the context of metric geometry, we derive explicit upper bounds for the entropy of all such self-shrinkers. Second, as an application we prove a smooth compactness theorem on the space of all such shrinkers. We also prove that there are only finitely many such self-shrinkers with an extra reflection symmetry.

Tree level Majorana neutrino mass from Type-1 × Type-2 Seesaw mechanism with Dark Matter

We propose a type of hybrid Seesaw model that combines Type-1 and Type-2 Seesaw mechanism in multiplicative way to generate tree level Majorana neutrino mass and provides a Dark Matter candidate. The model extends the Standard Model by extra gauge symmetry U(1)D and hidden sector consisted of chiral fermions and additional scalar fields. After spontaneous symmetry breaking, light neutrino masses are generated not only by exchange of the new heavy fermions as Type-1 Seesaw, but also by coupling to the naturally small induced vacuum expectation value of new heavy scalar as Type-2 Seesaw. An unbroken residue of U(1)D protects the lightest Dirac fermion required by anomaly cancellation in hidden sector from decaying, therefore giving rise to a Dark Matter candidate. Due to strong enough Seesaw suppression from our hybridization, new physics scale can be as low as TeV in this model and discovering signal from LHC data is possible in near future.

Scalar dark matter and muon g-2 in a model * *Supported by the National Natural Science Foundation of China (12075043, 12147205)

We consider a simple scalar dark matter model within the frame of gauged symmetry. A new gauge boson , as well as two scalar fields S and Φ, are introduced to the Standard Model (SM), where S and Φ are SM singlets but both carry charge. The real component and imaginary component of S can acquire different masses after spontaneously breaking symmetry, and the lighter one can play the role of dark matter, which is stabilized by an extra symmetry. We consider the possibility of light dark matter as well as the co-annihilation case in our model and present the current anomaly, Higgs invisible decay, dark matter relic density, and direct detection constraints on the parameter space. Direct detection gives the most stringent restriction on the model, and we found that although most of the parameter space is excluded, a mass region of a few GeV is still allowed where the co-annihilation process is also permitted in the model.

On the role of continuous symmetries in the solution of the three-dimensional Euler fluid equations and related models.

We review and apply the continuous symmetry approach to find the solution of the three-dimensional Euler fluid equations in several instances of interest, via the construction of constants of motion and infinitesimal symmetries, without recourse to Noether’s theorem. We show that the vorticity field is a symmetry of the flow, so if the flow admits another symmetry then a Lie algebra of new symmetries can be constructed. For steady Euler flows this leads directly to the distinction of (non-)Beltrami flows: an example is given where the topology of the spatial manifold determines whether extra symmetries can be constructed. Next, we study the stagnation-point-type exact solution of the three-dimensional Euler fluid equations introduced by Gibbon et al. (Gibbon et al. 1999 Physica D 132, 497–510. (doi:10.1016/S0167-2789(99)00067-6)) along with a one-parameter generalization of it introduced by Mulungye et al. (Mulungye et al. 2015 J. Fluid Mech. 771, 468–502. (doi:10.1017/jfm.2015.194)). Applying the symmetry approach to these models allows for the explicit integration of the fields along pathlines, revealing a fine structure of blowup for the vorticity, its stretching rate and the back-to-labels map, depending on the value of the free parameter and on the initial conditions. Finally, we produce explicit blowup exponents and prefactors for a generic type of initial conditions.This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 2)’.