The trinification model <Emphasis Type="Italic">SU</Emphasis>(3)<Superscript>3</Superscript> from orbifolds for fuzzy spheres

In this review, we consider an N = 4 supersymmetric SU(3N) gauge theory defined on the Minkowski spacetime. Then we apply an orbifold projection leading to an N = 1 supersymmetric SU(N)³ model, with a truncated particle spectrum. Then, we present the dynamical generation of (twisted) fuzzy spheres as vacuum solutions of the projected field theory, breaking the SU(N)³ spontaneously to a chiral effective theory with unbroken gauge group the trinification group, SU(3)³.     

Spontaneously broken quark helicity symmetry

We discuss the origin of chiral-symmetry breaking in the light-cone representation of QCD. In particular, we show how quark helicity symmetry is spontaneously broken in SU (N) gauge theory with massless quarks if that theory has a condensate of fermion light-cone zero modes. The symmetry breaking appears as induced interactions in an effective light-cone Hamiltonian equation based on a trivial vacuum. The induced interaction is crucial for generating a splitting between pseudoscalar and vector meson masses, which we illustrate with spectrum calculations in some 1 + 1-dimensional reduced models of gauge theory.     

Mass breaking in a relativistic quark model for mesons

We study symmetry breaking via quark mass differences in a relativistic quark model where mesons are built from heavy (m > 3 GeV) spin $\text{1}\text{2}$) quarks and antiquarks. The meson (squared-)mass differences are linearly related to the number of strange, charmed, etc. quarks in the mesons. We show that the previously assumed SU_n symmetry of the mesonic couplings holds, i.e., quark mass differences only show up in the masses of the external particles, not in the three meson vertex itself.     

From current to constituent quarks and the spin of the proton

We show in the context of an effective Lagrangian for baryons and pseudoscalar mesons how derivative couplings to Goldstone bosons modify the axial charges. Applying these considerations to constituent quarks we relate a modification of their axialU(1) charges to their internal structure which is represented here in term of a flavour singletφ ⁰ field attached to quarks. We end up with aSU (6)-type constituent quark model which describes the experimental results very well.     

Quark deconfinement at high temperature and thick vortices

First we describe Mack's effectiveZ(2) theory of quark confinement in theSU(2) lattice gauge theory at zero temperature. Then we show how quarks get liberated above a critical temperature, which has a numerical value somewhat below the glueball mass (in natural units).     

SO(N) supergravity and unification of all fundamental forces

From the group theoretical arguments, we find that among allSO(N) supergravitiesN=10 is the minimal supersymmetry group which unifies all fundamental forces of weak, electromagnetic, strong and gravitational interactions. The (super)symmetry is broken throughSO(10)→SU(3)?SU(2)?U(1)→SU(3)?U(1). All observed particles of the low energy physics (three generations of quarks and leptons, γ,Z, W ^± and gluons) and graviton can be minimally accomodated with the correctSU(3)?SU(2)?U(1) quantum numbers. Some characteristic predictions, which can be checked in the coming high energy experiments, are briefly discussed.     

Pion properties at finite isospin chemical potential with isospin symmetry breaking

Pion properties at finite temperature, finite isospin and baryon chemical potentials are investigated within the SU(2) NJL model. In the mean field approximation for quarks and random phase approximation fpr mesons, we calculate the pion mass, the decay constant and the phase diagram with different quark masses for the u quark and d quark, related to QCD corrections, for the first time. Our results show an asymmetry between μI 0 and μI 0 in the phase diagram, and different values for the charged pion mass(or decay constant) and neutral pion mass(or decay constant) at finite temperature and finite isospin chemical potential. This is caused by the effect of isospin symmetry breaking, which is from different quark masses.     

Chiral SU(2)×SU(2) model with infrared quark confinement

An SU(2)×SU(2) chiral quark model describing the properties and interaction of pions and scalar and vector mesons is considered. The confinement of quarks is introduced in the model by means of an infrared cut-off in the one-loop quark diagrams. This cutoff gives rise to the elimination of the unphysical thresholds of the quark-antiquark pair production. The π-a ₁ transitions are taken into account. The model conserves all low-energy theorems. The masses of mesons and the widths of the decays ρ → 2π and σ → 2π are calculated.     

Solution of a symmetry conserving chiral soliton model for nucleon and delta

The linear chiral soliton model is solved for nucleon and delta by constructing Fock states in the coherent pair approximation with correct spin and isospin properties. The quark configurations are those arising from theSU(2)×SU(2) coupling of three quarks in 1s-orbits. The overall Fock state is formed by the vector coupling of the quark configurations with the pion coherent state and thus avoids the use of the hedgehog ansatz. The sigma field is treated in the mean field approximation. Equations of motion for the quark, sigma and pion fields are solved in the static approximation. Soliton solutions are found with properties that are in reasonable agreement with those observed for the nucleon and delta including the axial vector coupling constant. With only components having zero and one unpaired pion in the coherent pair approximation the nucleon mass is found to be larger than that using the projected hedgehog approach.     

Geometrical basis for the Standard Model

The robust character of the Standard Model is confirmed. Examination of its geometrical basis in three equivalent internal symmetry spaces-the unitary planeC ², the quaternion spaceQ, and the real spaceR ⁴—as well as the real spaceR ³ uncovers mathematical properties that predict the physical properties of leptons and quarks. The finite rotational subgroups of the gauge groupSU(2) _L ×U(1) _Y generate exactly three lepton families and four quark families and reveal how quarks and leptons are related. Among the physical properties explained are the mass ratios of the six leptons and eight quarks, the origin of the left-handed preference by the weak interaction, the geometrical source of color symmetry, and the zero neutrino masses. The (u, d) and (c, s) quark families team together to satisfy the triangle anomaly cancellation with the electron family, while the other families pair one-to-one for cancellation. The spontaneously broken symmetry is discrete and needs no Higgs mechanism. Predictions include all massless neutrinos, the top quark at 160 GeV/c ², theb quark at 80 GeV/c ², and thet quark at 2600 GeV/c ².     

Quark masses and their hierarchies

Electroweak symmetry breaking is attributed to dynamical generation of quark masses. Quarksq (and leptonsl) are assumed to be produced by hypercolor confinement of preons at an intermediate scaleΛ _hc. Hierarchies observed in theq mass spectra can be explained by a BCS mechanism if the color interaction is enough asymptotically free and if residual ones emerging by the confinement are medium strong. The former assumption claims thatN≦4, whereN is the family number ofq andl. Dynamical equations to determineq masses and mixings are given, but they require knowledge on the physics atΛ _hc. A phenomenological approach is also made on the basis of anSU(7)×SU(7) chiral preon model withN=4. The mass ratiom _t/mb is related to (m _c/m _s)^ηB withη _B?1.1 andm _t'/mb' to (m _u/m _d)^ηA withη _A?1.4. In this scheme the fourth down quark is the heaviest (～ 110 GeV) and contributes dominantly toF ², whereF is the Fermi scale.     

Current algebra of quarks confined to a cavity

Equal-time commutators of fields with charges are calculated in a cavity approximation to the MIT bag model, with N flavours of non-interacting quarks confined to a rigid spherical cavity and SU(N) symmetry arbitrarily broken by mass terms. It is proved that inside the cavity the algebra is identical with that of free field theory, whilst on the boundary quark fields commute with axial charges. Vector divergences and sigma commutators belong to a $\text{(N,}\text{N}\text{) + (}\text{N}\text{, N)}$ multiplet of chiral SU(N) × SU(N). Axial divergences contain additional surface terms which do not contribute to sigma commutators. A non-strange quark mass in the range 20–44 MeV is required to give a value 30–70 MeV for the nucleon matrix element of the sigma commutator relevant to pion-nucleon scattering.     

Cavitation in holographic sQGP

We study the possibility of cavitation in the non-conformal N=^2?SU(N) theory which is a mass deformation of N=4SU(N) Yang-Mills theory. The second order transport coefficients are known from the numerical work using AdS/CFT by Buchel and collaborators. Using these and the approach of Rajagopal and Tripuraneni, we investigate the flow equations in a (1+1)-dimensional boost invariant set up. We find that the string theory model does not exhibit cavitation before phase transition is reached. We give a semi-analytic explanation of this finding.     

Heavy Quark Hadron Mass Scale

Without the spin interactions the hadron masses within a multiplet are degenerate. The light quark hadron degenerate multiplet mass spectrum is extended from the 3 quark ground state multiplets at J^P = 0⁻, ½⁺, 1⁻ to include the excited states which follow the spinorial decomposition of SU(2) × SU(2). The mass scales for the 4, 5, 6,… quark hadrons are obtained from the degenerate multiplet mass m₀/M = n²/α with n = 4, 5, 6,… The 4, 5, 6,… quark hadron degenerate multiplet masses follow by splitting of the heavy quark mass scales according to the spinorial decomposition of SU(2) × SU(2).     

The effective potential and the bound states for a class of two dimensional gauge theories

The effective potential is calculated for a two dimensionalU(N) gauge theory with scalar quarks to leading order in the 1/N expansion. If there is noφ ⁴ interaction present, the potential is unbounded from below. If theφ ⁴ interaction is present, the potential is bounded from below and there is an unbroken and a spontaneously broken symmetry phase. The bound state spectrum of the unbroken phase is very similar to that of anU(N) gauge theory without theφ ⁴ term.     

A relativistic quark model for baryons

The Bethe-Salpeter equation for the relativistic three quark bound state is solved for an instantaneous interaction in the ladder approximation. The particular solution obtained is valid for simple potentials in both the weak and strong binding situations. The general method for calculating matrix elements for the interaction of the bound state with an external electromagnetic field is presented. Particular attention is paid to the emergence of the nonrelativistic quark model interaction as the lowest order approximation in a perturbative expansion in the inverse quark mass. Relativistic corrections to this approximation are investigated, and their importance is seen to depend on the quark mass. For light quarks these corrections can be large, and to reproduce the proton magnetic moment, for instance, a substantial anomalous moment is necessary. The model has several encouraging features. The form factors with a harmonic potential have an asymptotic k^?2 behavior, and the relativistic corrections to the SU(6) results for the form factors are of the correct order of magnitude.     

Aspects of left-right symmetric models in superstring phenomenology

The general features of low-energy, rank-six left-right symmetric models as inspired by the superstring are examined. Particular attention is paid to the mass-mixing matrix of the exotic and downtype quarks. It is found that the class of models based on the groupSU(3) _C ×SU(2) _L ×SU(2) _N ×U(1) _L ×U(1) _R is plagued with the problem of unnatural fine tuning. Models based on the other left-right group, namelySU(3) _C ×SU(2) _L ×SU(2) _N ×U(1) _L ×U(1) _R , work rather well from the points of view investigated. In this case a parameter fitting is presented which is compatible with the lowering of the group rank by two units via radiative breaking, without conflicting either with weak universality or with lepton conservation. The unification scale comes in the 10¹⁷ GeV mass range, the intermediate (righthanded) scale is quite low, not exceeding the 10⁴ GeV range, and the Weinberg angle is correct. Good prospects are also obtained for proton decay and neutrino masses.     

Axial charges of octet baryons in two-flavor lattice QCD

We evaluate the strangeness-conserving NN, ΣΣ, ΞΞ, ΛΣ and the strangeness-changing ΛN, ΣN, ΛΞ, ΣΞ axial charges in lattice QCD with two flavors of dynamical quarks and extend our previous work on pseudoscalar-meson–octet-baryon coupling constants so as to include πΞΞ, KΛΞ and KΣΞ   coupling constants. We find that the axial charges have rather weak quark mass dependence and the breaking in SU(3)$\mathrm{SU}(3)$-flavor symmetry is small at each quark-mass point we consider.     

Heavy quark and gluino potentials to two loops

The static potentials for systems of a heavy quark and anti-quark, two gluinos and a quark and a gluino are computed for all possible color configurations of a SU(Nc) gauge group.