Local and global color symmetries of a symmetrical pattern

2019 ◽  
Vol 75 (5) ◽  
pp. 730-745
Author(s):  
Agatha Kristel Abila ◽  
Ma. Louise Antonette De Las Peñas ◽  
Eduard Taganap
Keyword(s):  
Symmetry Group ◽  
Local Symmetry ◽  
Global Symmetry ◽  
Color Symmetry ◽  
Usual Approach ◽  
Symmetrical Pattern ◽  
Symmetry Theory ◽  
Global Symmetry Group ◽  
Local Symmetries ◽  
Global And Local

This study addresses the problem of arriving at transitive perfect colorings of a symmetrical pattern {\cal P} consisting of disjoint congruent symmetric motifs. The pattern {\cal P} has local symmetries that are not necessarily contained in its global symmetry group G. The usual approach in color symmetry theory is to arrive at perfect colorings of {\cal P} ignoring local symmetries and considering only elements of G. A framework is presented to systematically arrive at what Roth [Geom. Dedicata (1984), 17, 99–108] defined as a coordinated coloring of {\cal P}, a coloring that is perfect and transitive under G, satisfying the condition that the coloring of a given motif is also perfect and transitive under its symmetry group. Moreover, in the coloring of {\cal P}, the symmetry of {\cal P} that is both a global and local symmetry, effects the same permutation of the colors used to color {\cal P} and the corresponding motif, respectively.

scholarly journals Goodness of Regularity in Dot Patterns: Global Symmetry, Local Symmetry, and Their Interactions

Perception ◽  
10.1068/p5794 ◽  
2007 ◽  
Vol 36 (9) ◽  
pp. 1305-1319 ◽  
Author(s):  
Massimo Nucci ◽  
Johan Wagemans
Keyword(s):  
Mirror Symmetry ◽  
Local Symmetry ◽  
Detection Task ◽  
Global Symmetry ◽  
Different Types ◽  
Operational Models ◽  
Local Mirror Symmetry ◽  
Axes Of Symmetry ◽  
Global And Local ◽  
Short Presentation

Goodness is a classic Gestalt notion defined as salience or perceptual strength of a given pattern. All operational models of goodness have assigned a central role to mirror symmetry but not much attention has been paid to the distinction between global and local mirror symmetry, and their possible interactions. We designed eight different types of dot patterns (all consisting of 80 dots), combining different numbers (0, 1, and 2) and relative orientations (parallel or orthogonal to each other) of local and global axes of symmetry (affecting 50% or 100% of the dots, respectively) at different absolute orientations (vertical and horizontal). Each of 640 trials consisted of a short presentation of a new dot pattern, which subjects had to classify as regular or random. We hypothesised that the overall goodness of patterns is not the simple sum of the amount of regularity present in them but depends on the cooperation and competition between symmetries. The results confirmed our hypothesis, showing that performance in this regularity-detection task did not increase in a linear way when some symmetries were added to other symmetries.

scholarly journals A Bosonisation of QCD and Realisations of Chiral Symmetry

1987 ◽  
Vol 40 (4) ◽  
pp. 499 ◽  
Author(s):  
CD Roberts ◽  
RT Cahill
Keyword(s):  
Symmetry Group ◽  
Chiral Symmetry ◽  
Functional Integral ◽  
Vacuum Field ◽  
Global Symmetry ◽  
Field Representation ◽  
Generating Functional ◽  
Global Symmetry Group ◽  
Vacuum Field Equation ◽  
Alternative Solutions

We employ the functional integral formalism to study quantum chromodynamics (QCD) with Nf quarks of zero bare mass. In addition to local SU(Nc) colour symmetry, this theory possesses exact global G = UdNf)@UR(Nf) chiral symmetry. We obtain an exact bilocal Bose field representation of the generating functional which, as we prove after establishing the manner in which the bilocal fields transform under G, preserves the global chiral symmetry. We demonstrate how a local Bose field representation of the generating functional may be obtained from the bilocal bosonisation. This provides a direct link between QCD and low energy meson phenomenological models. We utilise the bilocal bosonisation in the study of the dynamical breakdown of the global chiral symmetry group G. We derive the vacuum field equation from the exact bilocal Bose field effective action and discuss two alternative solutions: one corresponding to a Wigner-Weyl realisation of the global symmetry group G in which the vacuum configuration is invariant under G; the other to a mixed realisation in which the vacuum manifold is the coset space G/H = U A(Nf ), where H = Uv(Nf ) is a subgroup of G.

scholarly journals Models of hypercolor based on symplectic gauge group with three heavy vectorlike hyperquarks

2019 ◽  
Vol 28 (13) ◽  
pp. 1941002 ◽  
Author(s):  
Nikolay Volchanskiy ◽  
Vladimir Kuksa ◽  
Vitaly Beylin
Keyword(s):  
Higgs Boson ◽  
Standard Model ◽  
Symmetry Group ◽  
Gauge Group ◽  
Global Symmetry ◽  
Composite Higgs ◽  
Global Symmetry Group ◽  
The Standard Model ◽  
Dynamical Breaking ◽  
Partially Composite

We study possibilities to extend the Standard Model (SM) by three flavors of vectorlike heavy quarks in pseudoreal representation of symplectic hypercolor gauge group. This extension of SM predicts a rich spectra of heavy composite hypermesons and hyperbaryons (all of them carry integer spins) including 14 pseudo-Nambu–Goldstone states emerging in dynamical breaking of the global symmetry group of the H-quarks, [Formula: see text], to its Sp(6) subgroup. The properties of the lightest states depend strongly on the choice of heavy-quark hypercharges. Our focus is placed on the variants of the model with partially composite Higgs boson, i.e. the experimentally observed boson comprised the elementary SM Higgs and a mixture of H-hadrons.

scholarly journals Global Symmetries, Local Symmetries and Groupoids

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1905
Author(s):  
Michel Petitjean
Keyword(s):  
Global Symmetries ◽  
Local Symmetry ◽  
Color Symmetry ◽  
Graphs And Networks ◽  
Local Symmetries ◽  
Definition Of

Local symmetries are primarily defined in the case of spacetime, but several authors have defined them outside this context, sometimes with the help of groupoids. We show that, in many cases, local symmetries can be defined as global symmetries. We also show that groups can be used, rather than groupoids, to handle local symmetries. Examples are given for graphs and networks, color symmetry and tilings. The definition of local symmetry in physics is also discussed.

scholarly journals Pseudoscalar glueballs in the Klebanov-Strassler theory

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Dmitry Melnikov ◽  
Cornélio Rodrigues Filho
Keyword(s):  
Numerical Analysis ◽  
Symmetry Group ◽  
Global Symmetry ◽  
System Of Equations ◽  
Global Symmetry Group ◽  
Lattice Calculations ◽  
The Masses ◽  
Holographic Reconstruction

Abstract In this paper we describe a pseudoscalar subsector of the Klebanov-Strassler model. This subsector completes the holographic reconstruction of the spectrum of the lowest-lying glueball states, which are singlet under the global symmetry group SU(2) × SU(2). We derive the linearized supergravity equations for the pseudoscalar fluctuations and analyze their spectrum. The system of equations is shown to be compatible with six eigenmodes, as expected from supersymmetry. Our numerical analysis allows to reliably extract four of the corresponding towers. Their values match well the eigenvalues of the 0++ scalar states known from an earlier work. Assuming the masses of 0++ as a reference, we compare the lightest states of the holographic spectrum with lattice calculations in the quenched QCD at Nc = 3 and Nc = ∞.

A SCHEME FOR COMPLEMENTARITY AND HIGGS PHASE ANALYSES

1990 ◽  
Vol 05 (08) ◽  
pp. 531-542
Author(s):  
GONGRU LU ◽  
BING-LIN YOUNG ◽  
XINMIN ZHANG
Keyword(s):  
Simple Group ◽  
Symmetry Group ◽  
Phase Analysis ◽  
Dynamical Symmetry ◽  
Low Energy ◽  
Simple Groups ◽  
Global Symmetry ◽  
Global Symmetry Group ◽  
Composite Models ◽  
Dynamical Scheme

We introduce a simple dynamical scheme to supplement the complementarity and Higgs phase analyses of composite models with semi-simple metacolor groups. The critical couplings which signal the dynamical breakdown of the various simple groups contained in the metacolor semi-simple group determine the order of appearance of the condensates of the simple groups. Together with the Higgs phase analysis, it helps to determine the global symmetry of the fermion composite. The global symmetry group will eventually be gauged to form the low energy dynamical symmetry group of the composite.

scholarly journals Rank $Q$ E-string on spheres with flux

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Chiung Hwang ◽  
Shlomo Razamat ◽  
Evyatar Sabag ◽  
Matteo Sacchi
Keyword(s):  
Gauge Theory ◽  
Symmetry Group ◽  
Weyl Group ◽  
Global Symmetry ◽  
Dimensional Theory ◽  
Genus Zero ◽  
Four Dimensions ◽  
Global Symmetry Group ◽  
Cap Model ◽  
Zumino Model

We consider compactifications of rank \boldsymbol{Q}𝐐 E-string theory on a genus zero surface with no punctures but with flux for various subgroups of the \boldsymbol{\mathrm{E}_8\times \mathrm{SU}(2)}E8×SU(2) global symmetry group of the six dimensional theory. We first construct a simple Wess–Zumino model in four dimensions corresponding to the compactification on a sphere with one puncture and a particular value of flux, the cap model. Using this theory and theories corresponding to two punctured spheres with flux, one can obtain a large number of models corresponding to spheres with a variety of fluxes. These models exhibit interesting IR enhancements of global symmetry as well as duality properties. As an example we will show that constructing sphere models associated to specific fluxes related by an action of the Weyl group of \boldsymbol{\mathrm{E}_8}E8 leads to the S-confinement duality of the \boldsymbol{\mathrm{USp}(2Q)}USp(2𝐐) gauge theory with six fundamentals and a traceless antisymmetric field. Finally, we show that the theories we discuss possess an \boldsymbol{\mathrm{SU}(2)_{\text{ISO}}}SU(2)ISO symmetry in four dimensions that can be naturally identified with the isometry of the two-sphere. We give evidence in favor of this identification by computing the `t Hooft anomalies of the \boldsymbol{\mathrm{SU}(2)_{\text{ISO}}}SU(2)ISO in 4d and comparing them with the predicted anomalies from 6d.

scholarly journals Nilpotent symmetries as a mechanism for Grand Unification

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Lars Andersson ◽  
András László ◽  
Błażej Ruba
Keyword(s):  
Gauge Field ◽  
Scalar Product ◽  
Local Symmetry ◽  
Matter Field ◽  
Gauge Fields ◽  
Spacetime Symmetries ◽  
Invariant Scalar ◽  
Spacetime Manifold ◽  
Local Symmetries ◽  
Dilatation Group

Abstract In the classic Coleman-Mandula no-go theorem which prohibits the unification of internal and spacetime symmetries, the assumption of the existence of a positive definite invariant scalar product on the Lie algebra of the internal group is essential. If one instead allows the scalar product to be positive semi-definite, this opens new possibilities for unification of gauge and spacetime symmetries. It follows from theorems on the structure of Lie algebras, that in the case of unified symmetries, the degenerate directions of the positive semi-definite invariant scalar product have to correspond to local symmetries with nilpotent generators. In this paper we construct a workable minimal toy model making use of this mechanism: it admits unified local symmetries having a compact (U(1)) component, a Lorentz (SL(2, ℂ)) component, and a nilpotent component gluing these together. The construction is such that the full unified symmetry group acts locally and faithfully on the matter field sector, whereas the gauge fields which would correspond to the nilpotent generators can be transformed out from the theory, leaving gauge fields only with compact charges. It is shown that already the ordinary Dirac equation admits an extremely simple prototype example for the above gauge field elimination mechanism: it has a local symmetry with corresponding eliminable gauge field, related to the dilatation group. The outlined symmetry unification mechanism can be used to by-pass the Coleman-Mandula and related no-go theorems in a way that is fundamentally different from supersymmetry. In particular, the mechanism avoids invocation of super-coordinates or extra dimensions for the underlying spacetime manifold.

scholarly journals On Galilean Invariant and Energy Preserving BBM-Type Equations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 878
Author(s):  
Alexei Cheviakov ◽  
Denys Dutykh ◽  
Aidar Assylbekuly
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Numerical Simulations ◽  
Solitary Waves ◽  
Local Symmetry ◽  
Symmetry And Conservation Laws ◽  
Higher Order ◽  
Special Equation ◽  
Long Wave ◽  
Local Symmetries

We investigate a family of higher-order Benjamin–Bona–Mahony-type equations, which appeared in the course of study towards finding a Galilei-invariant, energy-preserving long wave equation. We perform local symmetry and conservation laws classification for this family of Partial Differential Equations (PDEs). The analysis reveals that this family includes a special equation which admits additional, higher-order local symmetries and conservation laws. We compute its solitary waves and simulate their collisions. The numerical simulations show that their collision is elastic, which is an indication of its S−integrability. This particular PDE turns out to be a rescaled version of the celebrated Camassa–Holm equation, which confirms its integrability.

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