Residual Symmetry Research Articles

Global symmetry-breaking and generalized theta-terms in Type IIB EFTs

A longstanding conjecture states that global symmetries should be absent in quantum gravity. By investigating large classes of Type IIB four-dimensional 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 effective field theories, we enlist the potential generalized global symmetries that could be present and explore how they are avoided. Crucial ingredients that arise in such effective field theories are generalized θ-terms. These introduce non-linear couplings between axion fields and topological terms quadratic in the gauge field strengths which break a large subset of the global symmetries. Additional residual global symmetries may further be broken by assuming the existence of some charged states. However, we illustrate that the presence of generalized θ-terms leads to a generalized Witten effect, which implies that the spectrum of charged states is constituted by an infinitely populated lattice. We further show that such a lattice is generated by the action of the monodromy transformation that characterizes the moduli space boundary near which the effective theory is defined.

2D-to-3D buckling transformability enabled reconfigurable metamaterials for tunable chirality and focusing effect

Recently, multifarious deformation approaches in nature have promoted dynamic manipulation for electromagnetic (EM) waves in metamaterials, and those representative strategies are mainly focused on the modulation of spectral parameters. Several works have also achieved tunable phase-gradient meta-devices. Here, to broaden the modulation freedom of mechanical deformation, we initially propose two reconfigurable metamaterials consisting of mirrored S-shaped meta-atoms selectively bonded on biaxially pre-stretched substrates. Planar meta-atoms with spin-insensitive transmittance are buckled into 3D morphologies to break residual symmetries by releasing the stress and to facilitate spin-dependent transmittance under circularly polarized incidence. Owing to the geometric anisotropy of S-shaped meta-atoms along the x and y axes, 3D chiral meta-atoms exhibit discriminate circularly cross-polarized transmittance under opposite spins. The underlying physical mechanism reveals that EM resonance originates from the excitation of electric dipoles and magnetic dipoles, and their cross coupling finally triggers the chiral effects of 3D meta-atoms. By introducing the gradient-phase design that keeps unchanged under various strains, two types of meta-atoms with specified orientations are interleaved to design a double-foci metalens, and its 2D-to-3D morphology transformation shortens the focusing length and facilitates the intensity change of two foci. Our approach in designing reconfigurable EM metamaterials with 2D-to-3D buckling transformability can be further extended toward terahertz even optical wavebands, and it may assist with deriving more applicable multi-functionalities in the aspects of imaging, sensing, and holograms.

Tensionless tales of compactification

We study circle compactifications of tensionless bosonic string theory, both at the classical and the quantum level. The physical state condition for different representations of BMS3, the worldsheet residual gauge symmetry for tensionless strings, admits three inequivalent quantum vacua. We obtain the compactified mass spectrum in each of these vacua using canonical quantization and explicate their properties.

’t Hooft–Polyakov monopoles and a general spherically symmetric solution of the Bogomolny equations

In this paper, we briefly review the ’t Hooft–Polyakov monopoles and the Bogomolny equations providing minimal energy field configurations in each topologically distinct sectors of monopole solutions. Then we consider the most general spherically symmetric ansatz for gauge fields depending on three arbitrary functions and find a general spherically symmetric solution of the Bogomolny equations. It depends on two integration constants and one arbitrary function on radius. The arbitrary function is proved to be related to the residual gauge symmetry of field configurations. In a general case, the spherically symmetric Euler–Lagrange equations are reduced to two nonlinear field equations for the two invariant functions. The Bogomolny–Prasad–Sommerfield solution is proved to be the only spherically symmetric nonsingular solution of field equations with finite energy.

Residual symmetry, CRE integrability and interaction solutions of two higher-dimensional shallow water wave equations

Two (3+1)-dimensional shallow water wave equations are studied by using residual symmetry and the consistent Riccati expansion (CRE) method. Through localization of residual symmetries, symmetry reduction solutions of the two equations are obtained. The CRE method is applied to the two equations to obtain new Bäcklund transformations from which a type of interesting interaction solution between solitons and periodic waves is generated.

Moduli trapping mechanism in modular flavor symmetric models

We discuss how the moduli in modular flavor symmetric models dynamically select enhanced symmetry points at which the residual modular symmetry renders extra matter fields massless. The moduli dynamics non-perturbatively produces the extra matter particles, which gives (time-dependent) effective potential that traps the moduli to enhanced symmetry points. We show analytic estimates of particle production rate consistent with numerical results, and the dynamics of moduli based on the analytic estimates.

The symmetric breathers and lumps of the Boussinesq equation using the Alice–Bob transformation and Hirota’s bilinear derivative method

Many two-place physical problems can be explicitly presented as related events model named Alice–Bob systems. In this paper, an integrable Alice–Bob Boussinesq system is introduced via the Boussinesq equation with parameters, which may meet the symmetry transformation of Psˆx (parity with a shift) and Tdˆt (time reversal with a delay). After constructing an Bäcklund transformation, the system has rich symmetry solutions with the aid of auxiliary functions. The structures of obtained soliton solutions, such as the breathers, lumps and their hybrids, are all satisfied the Pˆsx or Tˆdt symmetry. To illustrate the symmetric characteristic, some lower-order solutions and the related dynamic structures are explicitly presented. The residual symmetry and its finite transformation for this system are also verified.

Quark mass hierarchies and CP violation in A4 × A4 × A4 modular symmetric flavor models

We study A4× A4× A4 modular symmetric flavor models to realize quark mass hierarchies and mixing angles without fine-tuning. Mass matrices are written in terms of modular forms. At modular fixed points τ = i∞ and ω, A4 is broken to Z3 residual symmetry. When the modulus τ is deviated from the fixed points, modular forms show hierarchies depending on their residual charges. Thus, we obtain hierarchical structures in mass matrices. Since we begin with A4× A4× A4, the residual symmetry is Z3× Z3× Z3 which can generate sufficient hierarchies to realize quark mass ratios and absolute values of the CKM matrix |VCKM| without fine-tuning. Furthermore, CP violation is studied. We present necessary conditions for CP violation caused by the value of τ. We also show possibilities to realize observed values of the Jarlskog invariant JCP, quark mass ratios and CKM matrix |VCKM| simultaneously, if (10) adjustments in coefficients of Yukawa couplings are allowed or moduli values are non-universal.

Texture zeros of quark mass matrices at fixed point tau =omega in modular flavor symmetry

We study systematically derivation of the specific texture zeros, that is the nearest neighbor interaction (NNI) form of the quark mass matrices at the fixed point tau =omega in modular flavor symmetric models. We present models that the NNI forms of the quark mass matrices are simply realized at the fixed point tau =omega in the A_4 modular flavor symmetry by taking account multi-Higgs fields. Such texture zero structure originates from the ST charge of the residual symmetry Z_3 of SL(2, Z). The NNI form can be realized at the fixed point tau = omega in A_4 and S_4 modular flavor models with two pairs of Higgs fields when we assign properly modular weights to Yukawa couplings and A_4 and S_4 representations to three generations of quarks. We need four pairs of Higgs fields to realize the NNI form in A_5 modular flavor models.

Discrete dark matter mechanism as the source of neutrino mass scales

The hierarchy in scale between atmospheric and solar neutrino mass splittings is investigated through two distinct neutrino mass mechanisms from tree-level and one-loop-level contributions. We demonstrate that the minimal discrete dark matter mechanism contains the ingredients for explaining this hierarchy. This scenario is characterized by adding new RH neutrinos and SU(2)-doublet scalars to the Standard Model as triplet representations of an A4 flavor symmetry. The A4 symmetry breaking, which occurs at the electroweak scale, leads to a residual ℤ2 symmetry responsible for the dark matter stability and dictates the neutrino phenomenology. Finally, we show that to reproduce the neutrino mixing angles correctly, it is necessary to violate CP in the scalar potential.

Remarks on the two-point string amplitudes

The two-point string amplitude at tree level in flat spacetime reproduces the expected expression for free particles. This has been proven by Erbin, Maldacena and Skliros in [JHEP 07 (2019) 139] by two methods. Here, we provide an alternative proof of this result. Our method consists in considering a timelike Liouville direction as a regularization parameter, which suffices to break time translation invariance and, at the same time, to stabilize the residual conformal symmetry in the worldsheet. This allows taking a limit and restoring Poincare symmetry in a controlled way, thus reproducing the correct expression of the two-point amplitude.

Quark and lepton hierarchies from [formula omitted] modular flavor symmetry

We propose models in which the hierarchical structures of the masses and mixing in both quark and lepton sectors are explained by the S4′ modular flavor symmetry near the fixed point τ∼i∞. The model provides the first explicit example which explains hierarchies of both quarks and leptons from single modular flavor symmetry. The hierarchies are realized by powers of ϵ=e2πiτ/4=O(0.01) and 2Imτ∼5, where τ being the modulus. The small parameter ϵ plays a role of flavon in the Froggatt-Nielsen mechanism under the residual Z4T symmetry, and powers of 2Imτ in the Yukawa couplings are controlled by modular weights via the canonical normalization. The doublet quarks are identified to a S4′ triplet to explain the hierarchical structure of the quark mixing angles, while the doublet leptons are composed of three singlets for the large mixing angles in the lepton sector. We show that the S4′ modular symmetry alone can explain the hierarchies in both quark and lepton sectors by O(1) coefficients.

The residual symmetry, similarity reduction and n-th Bäcklund transformation for an extended (2+1)-dimensional shallow water wave system

The residual symmetry, similarity reduction and n-th Bäcklund transformation for an extended (2+1)-dimensional shallow water wave system

Post-inflationary axions: a minimal target for axion haloscopes

An axion-like-particle (ALP) in the post-inflationary scenario with domain wall number N > 1 can be dark matter if the residual ℤN symmetry has a small explicit breaking. Although we cannot determine the full dynamics of the system reliably, we provide evidence that such an ALP can account for the observed dark matter abundance while having a relatively small decay constant and consequently a possibly large coupling to photons. In particular, we determine the number of domain walls per Hubble patch around the time when they form using numerical simulations and combine this with analytic expectations about the subsequent dynamics. We show that the strongest constraint on the decay constant is likely to come from the dark matter ALPs being produced with large isocurvature fluctuations at small spatial scales. We also comment on the uncertainties on the dark matter small-scale structure that might form from these overdensities, in particular pointing out the importance of quantum pressure in the N = 1 case.

Non-local residual symmetry and soliton-cnoidal periodic wave interaction solutions of the KdV6 equation

The residual symmetry of the KdV6 equation is obtained by the Painlevé truncate expansion. Since the residual symmetry is non-local, five field quantities are introduced to localize it into the local one. Besides, the interaction solutions between solitons and cnoidal periodic waves of the KdV6 equation are constructed by making use of the consistent tanh expansion method. As an illustration, a specific interaction solution in the form of tanh function and Jacobian elliptic function is discussed both analytically and graphically.

Modeling covariance structures for genetic and non‐genetic effects in cowpea multi‐environment trials

AbstractIn cowpea breeding, multi‐environment trials are conducted to select lines with high yield. The occurrence of genetic and/or statistical imbalance is common in these experiments, in addition to the possibility of (co)variance between genetic and non‐genetic effects. We explore the restricted maximum likelihood/best linear unbiased prediction features to select the model with the most appropriated covariance structure and compare the results with the traditional model (homogenous variances and no covariances). Then, 17 inbred lines and three cultivars were evaluated in six experiments during two crop years in the semiarid zone of Northeast Brazil. The trait evaluated was the 100‐grain weight. We selected the best model considering the Akaike Information Criterion. The model with diagonal structure for the residual effects and heterogeneous compound symmetry for the genetic effects had the best fit. The predicted genetic gain of lines selected in this model was 1.18% higher compared to the traditional model. Modeling different (co)variance structures for genetic and non‐genetic effects is an efficient approach in selecting superior genotypes in multi‐environment trials in cowpea breeding.

Quark hierarchical structures in modular symmetric flavor models at level 6

We study modular symmetric quark flavor models without fine-tuning. Mass matrices are written in terms of modular forms, and modular forms in the vicinity of the modular fixed points become hierarchical depending on their residual charges. Thus modular symmetric flavor models in the vicinity of the modular fixed points have a possibility to describe mass hierarchies without fine-tuning. Since describing quark hierarchies without fine-tuning requires ${Z}_{n}$ residual symmetry with $n\ensuremath{\ge}6$, we focus on ${\mathrm{\ensuremath{\Gamma}}}_{6}$ modular symmetry in the vicinity of the cusp $\ensuremath{\tau}=i\ensuremath{\infty}$ where ${Z}_{6}$ residual symmetry remains. We use only modular forms belonging to singlet representations of ${\mathrm{\ensuremath{\Gamma}}}_{6}$ to make our analysis simple. Consequently, viable quark flavor models are obtained without fine-tuning.

Residual gauge symmetry in light-cone electromagnetism

We analyze the residual gauge freedom in light-cone electromagnetism in four dimensions. The standard boundary conditions involved in the so-called lc2formalism, which contains only the two physical degrees of freedom, allow for a subset of residual gauge transformations. We relax the boundary conditions imposed on the fields in order to obtain all the residual gauge transformations. We compute the canonical generators for Poincaré and gauge transformations with these relaxed boundary conditions. This enables us to distinguish between the trivial (proper) and large (improper) gauge transformations in light-cone electromagnetism. We then employ the Newman-Penrose formalism to identify the incoming and outgoing radiation fields. We comment on the quadratic form structure of light-cone Hamiltonians, often encountered in lc2 gauge theories.

Conformal (p, q) supergeometries in two dimensions

We propose a superspace formulation for conformal (p, q) supergravity in two dimensions as a gauge theory of the superconformal group OSp0(p|2; ℝ) × OSp0(q|2; ℝ) with a flat connection. Upon degauging of certain local symmetries, this conformal superspace is shown to reduce to a conformally flat SO(p) × SO(q) superspace with the following properties: (i) its structure group is a direct product of the Lorentz group and SO(p) × SO(q); and (ii) the residual local scale symmetry is realised by super-Weyl transformations with an unconstrained real parameter. As an application of the formalism, we describe mathcal{N} -extended AdS superspace as a maximally symmetric supergeometry in the p = q ≡ mathcal{N} case. If at least one of the parameters p or q is even, alternative superconformal groups and, thus, conformal superspaces exist. In particular, if p = 2n, a possible choice of the superconformal group is SU(1, 1|n) × OSp0(q|2; ℝ), for n ≠ 2, and PSU(1, 1|2) × OSp0(q|2; ℝ), when n = 2. In general, a conformal superspace formulation is associated with a supergroup G = GL× GR, where the simple supergroups GL and GR can be any of the extended superconformal groups, which were classified by Günaydin, Sierra and Townsend. Degauging the corresponding conformal superspace leads to a conformally flat HL× HR superspace, where HL (HR) is the R-symmetry subgroup of GL (GR). Additionally, for the p, q ≤ 2 cases we propose composite primary multiplets which generate the Gauss-Bonnet invariant and supersymmetric extensions of the Fradkin-Tseytlin term.

Equivariant Wavelets: Fast Rotation and Translation Invariant Wavelet Scattering Transforms.

Wavelet scattering networks, which are convolutional neural networks (CNNs) with fixed filters and weights, are promising tools for image analysis. Imposing symmetry on image statistics can improve human interpretability, aid in generalization, and provide dimension reduction. In this work, we introduce a fast-to-compute, translationally invariant and rotationally equivariant wavelet scattering network (EqWS) and filter bank of wavelets (triglets). We demonstrate the interpretability and quantify the invariance/equivariance of the coefficients, briefly commenting on difficulties with implementing scale equivariance. On MNIST, we show that training on a rotationally invariant reduction of the coefficients maintains rotational invariance when generalized to test data and visualize residual symmetry breaking terms. Rotation equivariance is leveraged to estimate the rotation angle of digits and reconstruct the full rotation dependence of each coefficient from a single angle. We benchmark EqWS with linear classifiers on EMNIST and CIFAR-10/100, introducing a new second-order, cross-color channel coupling for the color images. We conclude by comparing the performance of an isotropic reduction of the scattering coefficients and RWST, a previous coefficient reduction, on an isotropic classification of magnetohydrodynamic simulations with astrophysical relevance.