Baryon bound state in two-dimensional SU(N) gauge theory

The bound-state baryon problem with N quarks in an SU(N) gauge model of strong interactions is investigated in one-space and one-time dimensions. A study of planar diagrams yields color singlet “baryon” states of quarks that have infrared divergence-free mass spectra. The resulting integral equation turns out to be identical to the one obtained in a particular string model.     

Can extra dimensions accessible to the SM explain the recent measurement of anomalous magnetic moment of the muon?

We investigate whether models with flat extra dimensions in which SM fields propagate can give a significant contribution to the anomalous magnetic moment of the muon (MMM). In models with only SM gauge and Higgs fields in the bulk, the contribution to the MMM from Kaluza–Klein (KK) excitations of gauge bosons is very small. This is due to the constraint on the size of the extra dimensions from tree-level effects of KK excitations of gauge bosons on precision electroweak observables such as Fermi constant. If the quarks and leptons are also allowed to propagate in the (same) bulk (“universal” extra dimensions), then there are no contributions to precision electroweak observables at tree-level. However, in this case, the constraint from one-loop contribution of KK excitations of (mainly) the top quark to T parameter again implies that the contribution to the MMM is small. We show that in models with leptons, electroweak gauge and Higgs fields propagating in the (same) bulk, but with quarks and gluon propagating in a sub-space of this bulk, both the above constraints can be relaxed. However, with only one Higgs doublet, the constraint from the process b→sγ requires the contribution to the MMM to be smaller than the SM electroweak correction. This constraint can be relaxed in models with more than one Higgs doublet.     

SU(3) Local Gauge Field Theory as Effective Dynamics of Composite Gluons

The effective dynamics of quarks is described by a nonperturbatively regularized NJL model equation with canonical quantization and probability interpretation. The quantum theory of this model is formulated in functional space and the gluons are considered as relativistic bound states of colored quark-antiquark pairs. Their wave functions are calculated as eigenstates of hardcore equations, and their effective dynamics is derived by weak mapping in functional space. This leads to the phenomenological SU(3) gauge invariant gluon equations in functional formulation, i.e., the local gauge symmetry is a dynamical effect resulting from the dynamics of the quark model.     

On the roughening transition in abelian lattice gauge theories

We study the width of the confining string between static quarks in abelian lattice gauge theories using strong coupling expansions. We consider gauge groups Z_n and U(1) in 3 and 4 dimensions. This extends previous work with Lüscher, where SU(2) and Z₂ were studied. In ν = 3 dimensions we find evidence for a roughening transition. It is characterized by a divergence of the string width for an infinitely far separated quark-antiquark pair, while the string tension remains non-zero. In ν = 4 dimensions for the abelian groups we do not have evidence for a roughening transition away from a phase transition.     

High-temperature expansions for the free energy of vortices and the string tension in lattice gauge theories

We derive high-temperature cluster expansions for the free energy of vortices in SU(2) and Z₂ lattice gauge theories in 3 and 4 dimensions. The expected behaviour of the vortex free energy is verified. It obeys an area law behaviour. The coefficient of the area is shown to be equal to the string tension between static quarks. We calculate its expansion up to 12th order. For SU(2) in 4 dimensions the result is compared with Monte Carlo calculations of Creutz and is in good agreement at strong and intermediate coupling.     

Theories of quark confinement

It is conjectured that a non-Abelian gauge theory based on the color SU(3) group will confine quarks. Various techniques that have been applied to this question are reviewed. These include approximate methods based on strong coupling expansions of Hamiltonian and Euclidian lattice theories, instanton improvements on perturbation theory, and solutions of truncated Dyson-Schwinger equations for the gauge field propagator. Formal results based on electric-magnetic duality arguments and on the study of loop field theories are presented. Deconfinement at high temperatures, the inclusion of light quarks, and a possible reconciliation with a hypothetical discovery of free quarks are discussed.     

Discretized light cone quantization in a 3+1 dimensional valence model for quarkonium

Led by successes of the nonperturbative method of discretized light cone quantization (DLCQ) in 1+1-dimensional toy models, we study the feasibility of extending it to 3+1 dimensional theories. Within aSU(N _c ) nonabelian gauge theory, DLCQ is applied to a quarkonium system, where the Fock space has been truncated to the valence quark and antiquark only. In the light cone gauge the valenceq \(\bar q\) -model Hamiltonian matrix has an interesting structure which enables us to reduce the problem of diagonalization of some extremely large matrices to an amount of numerical labor already coped with in 1+1 dimensions. The model spectrum and the eigenfunctions are calculated independent of the order of the nonabelian gauge group, in special cases even analytically. The type of spectrum which appears after the calculation has been regularized covariantly may be interpreted as a sign that the quarks are confined in this model.     

Leading large N modification of QCD2 on a cylinder by dynamical fermions

We consider two-dimensional QCD on a cylinder, where space is a circle. We find the ground state of the system in case of massless quarks in a 1/Nexpansion. We find that coupling to fermions nontrivially modifies the large N saddle point of the gauge theory due to the phenomenon of “decompactification” of eigenvalues of the gauge field. We calculate the vacuum energy and the vacuum expectation value of the Wilson loop operator both of which show a nontrivial dependence on the number of quarks flavours at the leading order in 1/N.     

Toward a unification of “everything” with gravity

Combining the ideas of gauge interactions with a global supersymmetry, we build a unified model in six dimensions step by step, starting with a single generation of leptons and ending with three generations of leptons and colored quarks forming a supermultiplet characterized by a most general extensionN=8. The puzzle of supersymmetric partners, such as the gravitino, photino, s-leptons, and s-quarks, is seen in a new light. The supersymmetry is only a global one, whereas local supersymmetry and supergravity are replaced by the theory of gauge interactions and by the usual general relativity of Einstein.     

Composite electrodynamics

This paper solidifies the foundations for a singleton theory of light, first proposed two years ago. This theory is based on a pure gauge coupling of the scalar singleton field to the electromagnetic current. Like quarks, singletons are essentially unobservable. The field operators are not local observables and therefore need not commute for spacelike separation. This opens up possibilities for generalized statistics, just as is the case for quarks. It then turns out that a pure gauge coupling, in which ∂μφ(x) couples to the conserved current j^μ(x), generates real interactions— the effective theory is precisely ordinary electrodynamics in de Sitter space. Here we improve our theory and explain it in much more detail than before, adding two new results. (1) The concept of normal ordering in a theory with unconventional statistics is worked out in detail. (2) We have discovered the natural way of including both photon helicities. Quantization, it may be noted, is a study in representation theory of certain infinite-dimensional, nilpotent Lie algebras, of which the Heisenberg algebra is the prototype.     

Cylindrical gauge field configurations. A signal of confinement in QCD

An infrared approximation to the field equations of QCD is proposed which generates a mapping of configuration space into two dimensions (one time, one space dimension). The associated cylindrical gauge field configurations insure confinement whenever nontrivial interactions in two dimensions remain. This feature distinguishes abelian from nonabelian gauge theories.     

Geometric interpretation of hadronization model

A hadronization model termed as geometric dielectric confinement model is described. The model describes the charmed meson decays quite successfully. In the model we assume that the non-abelian gauge field describing the colour force simulates the effect of a medium having space-dependent dielectric constant. The quarks produced in weak decays move in the dielectric medium such that they are free in limited region of space (r⋍0) and cannot appear as asymptotic states resulting in hadronization. It is found that the dielectric medium resembles anti-desitter microuniverse and the quarks behave essentially as free particles damped by gaussian distribution. The model reproduces from a single Lagrangian the quark motion as well as the form of dielectric function.     

The interquark potential: SU(2) colour gauge theory with fermions

Including dynamical fermions in the Monte Carlo simulation of the SU(2) gauge theory, the potential between static quarks is investigated on a 16×8³ lattice. The Coulomb part of the force is stronger as compared with the pure gauge field theory. At large distances indications are found for a deviation from the linear rise of the potential, expected from a break-up of the flux tube between the heavy quarks through spontaneous creation of light quark pairs.     

Diquark mass differences from unquenched lattice QCD

We calculate diquark correlation functions in the Landau gauge on the lattice using overlap valence quarks and 2+1-flavor domain wall fermion configurations. Quark masses are extracted from the scalar part of quark propagators in the Landau gauge. The scalar diquark quark mass difference and axial vector scalar diquark mass difference are obtained for diquarks composed of two light quarks and of a strange and a light quark. The light sea quark mass dependence of the results is examined. Two lattice spacings are used to check the discretization effects.The coarse and fine lattices are of sizes 24~3×64 and 32~3×64 with inverse spacings 1/a = 1.75(4) Ge V and 2.33(5) Ge V,respectively.     

A reduced hamiltonian model for U(∞) gauge theories

A reduced version of the Kogut-Susskind gauge theory is presented for U(∞) gauge theories. The reduced hamiltonian , where V_ij=trU_iD_iD_jD_j(U_iD_j) ⁺ (U_iD_j)⁺, is obtained by representing the group of space translations in the diagonal part of U(∞) U(∞). The space of states is invariant to the reduced gauge transformation U_i→ωU_iD_iω⁺D_i⁺ and the scalar product carries a gauge invariant constraint on U_i The hamiltonian is also expr essed in terms of the string variables of Bars. We present the linear potential between static quarks at strong coupling and sketch the weak coupling expansion.     

Parity violating neutral currents in a left-right symmetric gauge model

We consider parity violating effects in the neutral sector of a left-right symmetric SU(2)_L × SU(2)_R × U(1) gauge model of weak and electromagnetic interaction. With four quarks and four leptons, the parity violating optical rotation in atoms is estimated to be about an order of magnitude smaller (and of opposite sign) compared to the Salam-Weinberg (SW) model prediction. However, with new quarks and leptons this effect can be arranged to be even smaller. Weak-electromagnetic interference effects are quantitatively different from those found in the SW model. A unified gauge theory which embeds the left-right symmetric gauge model is briefly discussed.     

A model of unified quantum chromodynamics and Yang-Mills gravity

Based on a generalized Yang-Mills framework, gravitational and strong interactions can be unified in analogy with the unification in the electroweak theory. By gauging T (4) × [SU (3)] color in flat space-time, we have a unified model of chromo-gravity with a new tensor gauge field, which couples universally to all gluons, quarks and anti-quarks. The space-time translational gauge symmetry assures that all wave equations of quarks and gluons reduce to a Hamilton-Jacobi equation with the same ’effective Riemann metric tensors’ in the geometric-optics (or classical) limit. The emergence of ef f ective metric tensors in the classical limit is essential for the unified model to agree with experiments. The unified model suggests that all gravitational, strong and electroweak interactions appear to be dictated by gauge symmetries in the generalized Yang-Mills framework.     

Colour gluons and scaling in a unified gauge model

Deep inelastic weak and electromagnetic processes are considered within the parton framework taking the partons to be integrally charged quarks and coloured gluons. Despite the participation of the spin-one gluons in these processes, scaling is shown to be maintained by treating the problem in a unified gauge model based on the groupSU (3)_colour⊗SU _L (2)⊗U(1). This is a consequence of the vector-dominance type of couplings between the gluons and the weak or electromagnetic vector bosons which are induced by the spontaneous breakdown of gauge symmetry. As a further consequence it is found that in the asymptotic region far above the gluon masses the colour octet parts of the weak and electromagnetic currents of the quarks are damped so that, in particular, the integrally charged quarks behave as fractionally charged quarks in this region.     

Argyres-Seiberg Duality and the Higgs Branch

We demonstrate the agreement between the Higgs branches of two ${\mathcal{N}=2}We demonstrate the agreement between the Higgs branches of two N=2{\mathcal{N}=2} theories proposed by Argyres and Seiberg to be S-dual, namely the SU(3) gauge theory with six quarks, and the SU(2) gauge theory with one pair of quarks coupled to the superconformal theory with E ₆ flavor symmetry. In mathematical terms, we demonstrate the equivalence between a hyperk?hler quotient of a linear space and another hyperk?hler quotient involving the minimal nilpotent orbit of E ₆, modulo the identification of the twistor lines.