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.

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 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.

The Superstring Propagator and the Signature of Space-Time

1997 ◽  
Vol 12 (14) ◽  
pp. 987-998 ◽  
Author(s):  
M. D. Pollock
Keyword(s):  
Wave Function ◽  
Apparent Horizon ◽  
Scalar Particle ◽  
Space Time ◽  
Functional Integral ◽  
Global Symmetry ◽  
Hamiltonian Constraint ◽  
Superstring Theory ◽  
Acceptable Solution ◽  
Higher Derivative

The Faddeev (Newton–Wigner) propagator K for the heterotic superstring theory is derived from the Wheeler–DeWitt equation for the wave function of the Universe Ψ, obtained in the four-dimensional (mini-superspace) Friedmann space-time ds2=dt2-a2(t)dx2, after reduction from the ten-action. The effect of higher-derivative terms ℛ2 is to break the local invariance under time reparametrization to a global symmetry t→λt, and consequently there are no ghost or gauge-fixing contributions, a functional integral over the (constant) Lagrange multiplier λ being sufficient to enforce the Hamiltonian constraint implicitly. After Wick rotation of the time, [Formula: see text], the only physically acceptable solution for K decreases exponentially on the Planck time-scale ~ t P , explaining from the quantum cosmological viewpoint why the signature of space-time is Lorentzian rather than Euclidean. This is analogous to the case of the (two-dimensional) free relativistic scalar particle, discussed recently by Redmount and Suen, who found that the propagator decreases exponentially outside the light-cone on the scale of the Compton wavelength of the particle (in accordance with the Heisenberg indeterminacy principle). These two seemingly different forms of acausality are thus physically excluded in the same way. The propagator for the Schwarzschild black hole of mass M is also obtained from the Schrödinger equation for the wave function on the apparent horizon, due to Tomimatsu, and the Hawking temperature T H =(8π M)-1 is derived from the Euclidean form of this equation.

ON GRAVITO-ELECTROMAGNETIC DUALITY IN GENERAL RELATIVITY

1999 ◽  
Vol 14 (12) ◽  
pp. 759-763 ◽  
Author(s):  
NARESH DADHICH
Keyword(s):  
General Relativity ◽  
Field Equation ◽  
Gravitational Constant ◽  
Electromagnetic Theory ◽  
Vacuum Field ◽  
Vacuum Equation ◽  
Riemann Curvature ◽  
Duality Transformation ◽  
Duality Symmetry ◽  
Vacuum Field Equation

In analogy with the electromagnetic theory, we resolve the Riemann curvature into electric and magnetic parts and consider the analogous duality transformation which keeps the Einstein action for vacuum invariant. It is remarkable that the duality symmetry of the action also leads to the vacuum field equation without cosmological constant. Further invariance of the vacuum equation and the action under the gravito-electric duality require gravitational constant to change sign.

scholarly journals Dynamical Symmetries of the 2D Newtonian Free Fall Problem Revisited

Symmetry ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 27
Author(s):  
Tuong Trong Truong
Keyword(s):  
Symmetry Group ◽  
Anharmonic Oscillator ◽  
Symmetry Algebra ◽  
Functional Space ◽  
Free Fall ◽  
Dynamical Symmetry ◽  
Functional Integral ◽  
Theoretical Physics ◽  
Classical Level ◽  
Dynamical Symmetries

Among the few exactly solvable problems in theoretical physics, the 2D (two-dimensional) Newtonian free fall problem in Euclidean space is perhaps the least known as compared to the harmonic oscillator or the Kepler–Coulomb problems. The aim of this article is to revisit this problem at the classical level as well as the quantum level, with a focus on its dynamical symmetries. We show how these dynamical symmetries arise as a special limit of the dynamical symmetries of the Kepler–Coulomb problem, and how a connection to the quartic anharmonic oscillator problem, a long-standing unsolved problem in quantum mechanics, can be established. To this end, we construct the Hilbert space of states with free boundary conditions as a space of square integrable functions that have a special functional integral representation. In this functional space, the free fall dynamical symmetry algebra is shown to be isomorphic to the so-called Klink’s algebra of the quantum quartic anharmonic oscillator problem. Furthermore, this connection entails a remarkable integral identity for the quantum quartic anharmonic oscillator eigenfunctions, which implies that these eigenfunctions are in fact zonal functions of an underlying symmetry group representation. Thus, an appropriate representation theory for the 2D Newtonian free fall quantum symmetry group may potentially open the way to exactly solving the difficult quantization problem of the quartic anharmonic oscillator. Finally, the initial value problem of the acoustic Klein–Gordon equation for wave propagation in a sound duct with a varying circular section is solved as an illustration of the techniques developed here.

Sign in / Sign up

Export Citation Format

Share Document