Results For SU Research Articles

Exact results in SO(11) SUSY gauge theories with spinor and vector matter

We investigate the confining phase vacuum structure of supersymmetric SO(11) gauge theories with one spinor matter field and N f ≤ 6 vectors. We describe several useful tricks and tools that facilitate the analysis of these chiral models and many other theories of similar type. The forms of the N f = 5 and N f = 6 quantum moduli spaces are deduced by requiring that they reproduce known results for SU(5) SUSY QCD along the spinor flat direction. After adding mass terms for vector fields and integrating out heavy degrees of freedom, we also determine the dynamically generated superpotentials in the N f ≤ 4 quantum theories. We close with some remarks regarding magnetic duals to the N f ≥ 7 electric SO(11) theories.

Results in SU(2) × SU(2) super symmetric gauge theories

We consider N = 1 SU (2) × SU (2) supersymmentric gauge theory with n matter fields transforming in the (2,2) representation and one matter field transforming in the (1, 3) representation. For n = 0, 1, 2 we derive an exact super potential. Various consistency checks are applied on the result. For n = 2 we obtain signals that at special values of the light fields additional degrees of freedom become massless.

A comparison of tomography and zonography during intravenous urography

Purpose: Wide angle tomography is used regularly during excretion urography to overcome the problem of bowel shadows obscuring the kidneys. Because Methods: A specially constructed renal phantom was used to establish radiation dose levels for tomography and zonography. Subjective analyses on su Results: Statistical analysis demonstrated that fewer exposuresper intravenous urography examination were necessary for zonography (1.6) compared w Conclusions: This investigation suggests zonography should replace tomography for routine excretion urography with potential benefits for patient d

Representations of quantum SU(3)

The problem of constructing representations of the quantum group SU(3)q is considered. This algebra may be constructed from two sets of SU(2)q generators, oriented at an angle of 120° from each other. If one makes use of known results for SU(2)q, the problem reduces to finding the transformation matrices between two sets of basis vectors, in each of which the Casimir operator for one of the SU(2)q’s is diagonal. Two simple prescriptions are given for finding these matrices in a general case, using a convenient set of variables. An exact solution is given for all irreducible representations in which the maximum weight multiplicity is 2.

LEVEL-ONE SU(N) WZNW MODELS ON HIGHER-GENUS RIEMANN SURFACES

Using factorization properties and fusion rules, we find the higher-genus partition function and two-point correlators for the SU (N)1 WZNW model. The result has simple form in terms of higher-genus theta functions on the group manifold. The previously known results of SU (2)1 and SU (3)1 are also obtained as special cases. This method, combined with other considerations such as modular invariance, can be extended to the nonsimply laced groups and higher-level WZNW models.

Scaling and asymptotic scaling in the SU(2) gauge theory

We determine the critical couplings for the deconfinement phase transition in SU(2) gauge theory on N τ × N σ 3 lattices with N τ = 8 and 16 and N σ varying between 16 and 48. A comparison with string tension data shows scaling of the ratio T c/√ σ in the entire coupling regime ß = 2.30−2.75, while the individual quantities still exhibit large scaling violations. We find T c/√ σ = 0.69(2). We also discuss in detail the extrapolation of T c /Λ MS and √σ/Λ MS to the continuum limit. Our result, which is consistent with the above ratio, is T c /Λ MS =1.23(11) and √σ/Λ MS =1.79(12) . We also comment upon corresponding results for SU(3) gauge theory and four-flavour QCD.

Smallness of gluon coupling to constituent quarks in baryons and validity of nonrelativistic quark model.

A study of the parametrization of baryon masses and other quantities leads to a ratio \ensuremath{\cong} ⅕ for two-gluon-exchange versus one-gluon-exchange terms between two constituent quarks in a baryon. This fact (plus the factor 3 reduction from each additional order in flavor breaking) explains the success, to a part per thousand, of a new baryon mass formula [Phys. Rev. Lett. 68, 139 (1992)]. It also explains why the results of SU(3) that neglect second-order flavor breaking (such as the Gell-Mann-Okubo baryon mass formula) work much better than expected. Finally the general parametrization, plus the above reduction factors, clarify why the naive nonrelativistic quark model (NRQM) is quantitatively fairly good. The reasons are twofold: (a) The structure of the general parametrization (an exact consequence of any QCD-like relativistic field theory) is similar to that of the NRQM; (b) the smallness of the gluon coupling and the reduction factor due to flavor imply that the additive (one-body) terms in the parametrization prevail on the two-body terms and the latter on the three-body ones, the typical feature of the naive NRQM.

Electron scattering multipoles for symplectic shell model applications

The charge and current density multipoles used in calculating electron scattering form factors are given in a form suitable for second-quantized SU (3) shell-model applications. The expressions are exact representations of the density multipoles, extend over all major oscillator shells, and are tailored for symplectic shell-model applications. Through a SU(3) tensor decomposition of these multipoles, the importance of considering multiple irreps in symplectic model calculations for ds-shell nuclei is explored, as well as the extent to which higher shell correlations will influence form factor predictions. Results for SU(3) model applications to 20Ne, 22Ne, and 24Mg are given and the significance of the theory for symplectic model applications is discussed. The relation of this general fermion formulation to a restricted harmonic oscillator boson representation is also demonstrated.

Contraction of Lie algebra representations

Motivated by an example of Inönü and Wigner, a general procedure for the contraction of irreducible unitary representations of semisimple compact Lie algebras is given. In this situation, contractions mean generalized Inönü–Wigner contractions. In particular, this means that by a simple limiting process, one obtains representations of nonsemisimple noncompact Lie algebras. As examples, a general treatment of SO(3) is given as well as some results for SU(3).

Lattice calculation of baryonic electromagnetic form factors

Lattice QCD provides a promising method of addressing the elusive non-perturbative aspect of hadronic physics. It may be used in an investigation of underlying quark dynamics which is not based on model dependent calculations. The study of electromagnetic form factors allows a comparison of the predictions of the quark model and the Skyrme model with those of non-perturbative model independent approaches such as Lattice QCD and the QCD Sum Rule method. The first lattice calculations of electroma~etic form factors focussed on the electric form factor of the pion with SU(2) color [I]. These were later extended to SU(3) color [2]. Calculations of the electric form factor of the proton followed [3]. Most recently, both the electric and magnetic form factors of the proton and neutron were calculated [4]. Here the analysis of reference [4] is extended to calculate the electromagnetic form factors of the octet baryons. Electric and magnetic form factors have been calculated (from twoand three-point baryon correlation functions) on a quenched 24 x 12 x 12 x 24 lattice with p = 5.9. A small value of momentum transfer (I&X = 2x/24) was investigated for three values of quark mass (K = 0.152,0.154,0.156). nom these form factors, electric and magnetic charge radii, magnetic moments and magnetic transition moments have been extracted. More details of the method of calculation as outlined in reference j4] are provided in reference [5]. The results illustrate the manner in which quarks account for the electromagnetic structure of baryons. An outstanding problem of hadronic physics has been to explain the magnetic moments of baryons. In figure 1, we have collected recent results of alternative approaches to the strong interaction. The results of SU(6) symmetry, the sum rule approach [S], our lattice calculation, a recent quark model [7], and the Skyrme model [8] are compared to experimental ratios of magnetic moments. (The experimental and sum rule results for Co are obtained using the SU(2) relationship ~E:D = (PC+ + lc-)f2.) The quark model results differ significantly from those of the simple quark model only in the value of the Cmagnetic ratio which has been shifted from -0.391 to -0.505. The quark model (with four parameters) does not reproduce the magnetic moment ratios as well as the sum rule or lattice results. Only the N and A magnetic ratios are accurately reproduced. The Skyrme model (with two parameters) reverses the order of many of the SU(6) partners. The results of the sum rule approach (which has vacuum susceptibility parameters optimized to give the best agreement with experimental magnetic moments) are very similar to those of the lattice with the exception of the 2where non-perturbative and strange-quark mass effects are very large in the sum rule calculation.

Finite-size effects for nested Bethe ansatz equations: analytical and numerical results for SU(N) and O(2N) magnets

The author studies the finite-size effects in the SU(N) and O(2N) Bethe ansatz equations for ground-state configurations. He compares his results with a numerical solution of the associated Bethe ansatz equations.

Some results of SU(2) spinorial lattice gravity

The author reports on the status of the closure problem for the regularised constraint operators of general relativity within the SU(2) spinorial Hamiltonian lattice gauge theory framework constructed in a previous work. The author describes how the diffeomorphism subalgebra is recovered upon removal of the regulator. Comparisons are drawn with the work of Rovelli and Smolin (1988) in the continuum, and it is described how the lattice framework provides a natural analogue of the sector of the physical state space that they describe.

PROTON DECAY INCLUDING EXTRA Z0 BOSONS

There exists an apparent discrepancy between proton decay experiment and simplest SU(5) prediction. We suggest a scheme: if there exists an extra Z0 boson, then the experimental value of the proton decay may be calculated from GUT and the good results of SU(5) can be preserved. The increasing fermions will not be bizarre.

Orthogonal polynomial expansions for finite group transformations

A simple tractable method for calculating finite group transformations is given. This is achieved by introducing orthogonal polynomial functions of the generating element of the transformation. The polynomials, which are finite in number because the Cayley-Hamilton theorem applies, depend only on the conjugacy class of the transformation. Orthogonality is defined with respect to the trace operation. Results for SU(2) and the defining representation of SU(3) are examined in some detail.

Stochastic quantization for numerical simulation

An algorithm for numerical simulation, based on stochastic quantization, is presented. Results for SU( N)×SU( N) matrix models for N = 2,3and4 in various dimensions are discussed.

Some results for SU(N) gauge-fields on the Hypertorus

We show how to prove and to understand the formula for the “Pontryagin” indexP for SU(N) gauge fields on the HypertorusT4, seen as a four-dimensional euclidean box with twisted boundary conditions. These twists are defined as gauge invariant integers moduloN and labelled byNμv (=−Nμv). In terms of these we can write (ν∈#x2124;) $$P = \frac{1}{{16\pi ^2 }}\int {Tr(G_{\mu v} \tilde G_{\mu v} )d_4 x = v + \left( {\frac{{N - 1}}{N}} \right) \cdot \frac{{n_{\mu v} \tilde n_{\mu v} }}{4}} $$ . Furthermore we settle the last link in the proof of the existence of zero action solutions with all possible twists satisfying\(\frac{{n_{\mu v} \tilde n_{\mu v} }}{4} = \kappa (n) = 0(\bmod N)\) for arbitraryN.

Monte Ćarlo calculations and a model of the phase structure for gauge theories on discrete subgroups of SU(2)

A Monte Carlo technique is used to evaluate path integrals for lattice gauge theories with gauge groups given by the SU(2) images of the rotational symmetries of a tetrahedron, a cube, and an icosahedron, called $\overline{T}$, $\overline{O}$, and $\overline{I}$, respectively. The coupling-constant dependence of the mean action per plaquette provides evidence for two phases, in each of these theories, separated by a first-order phase transition. The critical gauge coupling constant moves toward zero as the order of the group is increased. The mean plaquette action, the expectations of square gauge loops, and an estimate of the string tension for the largest group $\overline{I}$ agree with Creutz's results for SU(2) over a wide range of coupling constants. A model for the phase transitions in $\overline{T}$, $\overline{O}$, $\overline{I}$, and ${Z}_{N}$ is discussed which predicts critical coupling constants close to the observed values and suggests, as expected, that these transitions are a special property of gauge theories over discrete groups.

Lorentz-Invariance Algebraization of Hadron Vertex Function in SU(3)

It is shown that, in the exact SU(3) limit and under plausible assumptions, the matrix elements of the SU(3) axial-vector currents taken between two hadron states at rest form a closed algebra isomorphic to SO(9, 3). Some remarks are made on previous results for SU(2) axial-vector currents.

Electromagnetic properties of the baryons in the Capps bootstrap model

The electromagnetic properties of the P-wave baryons are calculated using the Capps bootstrap assumptions f or the photo-meson production processes in the static model. The magnetic moments are expressed in terms of two free parameters which are fitted to the magnetic moments of the proton and neutron. The electromagnetic mass differences following from this bootstrap scheme are completely consistent with the results of SU(6). It is pointed out that Capps bootstrap assumptions completed by various requirements can reproduce exactly the results following from all group-theory treatments.