Version Of SU Research Articles

Gauged spinning models with deformed supersymmetry

New models of the SU(2|1) supersymmetric mechanics based on gauging the systems with dynamical (1,4,3) and semi-dynamical (4,4,0) supermultiplets are presented. We propose a new version of SU(2|1) harmonic superspace approach which makes it possible to construct the Wess-Zumino term for interacting (4,4,0) multiplets. A new N=4 extension of d=1 Calogero-Moser multiparticle system is obtained by gauging the U(n) isometry of matrix SU(2|1) harmonic superfield model.

EXTRA NEUTRAL GAUGE BOSON FROM THE 3-3-1 MODEL AND THE SPIN CORRECTION OF TOP QUARK PAIR PRODUCTION AT THE ILC

In the off-diagonal basis, we explore the effects of extra neutral gauge boson Z' predicted in two versions of SU (3)C × SU (3)L × U (1)X model on the spin configuration of the top quark pair production in the high energy linear e+e- collider (ILC). Our numerical results show that, the cross sections for the suppressed spin configurations can be enhanced with the effects of the Z' boson through the modification of the spin configuration by producing enough top quark pairs to be measured in the future ILC experiments, which provides the way to observe the effects of Z' predicted in the 3-3-1 model and discriminate the various versions of 3-3-1 model.

Reformulating SU(N) Yang-Mills Theory Based on Change of Variables

We propose a new version of SU(N) Yang-Mills theory reformulated in terms of new field variables which are obtained by a nonlinear change of variables from the original Yang-Mills gauge field. The reformulated Yang-Mills theory enables us to study the low-energy dynamics by explicitly extracting the topological degrees of freedom such as magnetic monopoles and vortices to clarify the mechanism for quark confinement. The dual superconductivity in Yang-Mills theory is understood in a gauge-invariant manner, as demonstrated recently by a non-Abelian Stokes theorem for the Wilson loop operator, although the basic idea of this reformulation is based on the Cho-Faddeev-Niemi decomposition of the gauge potential. §1. Introduction The original Yang-Mills theory 1) is formulated in terms of the Yang-Mills gauge field. This formulation is suitable for studying the high-energy dynamics of YangMills theory. For instance, it is well known that the perturbation theory in the coupling constant developed in terms of the Yang-Mills field is very powerful in the ultraviolet region due to its asymptotic freedom. In the low-energy region, however, we encounter the strong coupling problem, and its description in terms of the YangMills gauge field is no longer valid. In studying the low-energy dynamics of YangMills theory and quantum chromodynamics (QCD), it is important to specify the most relevant degrees of freedom for the phenomenon in question. Quark confinement as a typical phenomenon in the low-energy dynamics caused by strong interactions is believed to be explained by topological defects including magnetic monopoles, vortices and merons. This motivates us to devise another formulation of Yang-Mills theory in terms of new variables reflecting the topological degrees of freedom.

NON-ABELIAN STOKES THEOREM AND QUARK CONFINEMENT IN SU(3) YANG–MILLS GAUGE THEORY

We derive a new version of SU (3) non-Abelian Stokes theorem by making use of the coherent state representation on the coset space SU (3)/ U (1) × U (1)) = F2, the flag space. Then we outline a derivation of the area law of the Wilson loop in SU (3) Yang–Mills theory in the maximal Abelian gauge (the detailed exposition will be given in a forthcoming article). This derivation is performed by combining the non-Abelian Stokes theorem with the reformulation of the Yang–Mills theory as a perturbative deformation of a topological field theory recently proposed by one of the authors. Within this framework, we show that the fundamental quark is confined even if G = SU (3) is broken by partial gauge fixing into H = U (2) just as G is broken to H = U(1) × U(1). An origin of the area law is related to the geometric phase of the Wilczek–Zee holonomy for U (2). Abelian dominance is an immediate by-product of these results and magnetic monopole plays the dominant role in this derivation.

R-parity violation and Peccei-Quinn symmetry in GUTs

We address the question whether it is possible in GUTs to obtain R-parity violation with a large ΔL ΔB hierarchy of strengths so that the proton is stable while phenomenologically interesting L-violation is present. We consider versions of SU(5) with a built-in Peccei-Quinn symmetry spontaneously broken at an intermediate scale. The PQ symmetry and the field content guarantee a large suppression of the effective B-violating terms by a factor Λ PQ 3 M PM X 2 while the effective L-violating terms stay large.

Supersymmetric quantum mechanics for inverse square potentials

In elementary particle physics, supersymmetry (SUSY) (Wess and Zumino, 1974) is a symmetry which relates half-integral spin particles (fermions) to particles with integral spin (bosons). Using the supersymmetric version of SU(5) or SO(10), it was possible to unify electromagnetic, weak, and strong interactions. There is no experimental evidence for the existence of new SUSY particles in nature. On the other hand, applications of SUSY have been found in nuclear and condensed matter physics as well. Applications of supersymmetry in nonrelativistic quantum mechanics was first discussed by Witten (1981). The aim of this paper is to analyze the inverse square potentials using supersymmetric quantum mechanics. First we discuss how to construct supersymmetric algebra in quantum mechanics. Introducing SUSY quantum mechanics, then we analyze inverse square potentials in that context. Supersymmetric quantum mechanics has a close relationship to supersymmetric field theory. Supersymmetric one-particle quantum mechanics serves as a model for the investigation of spontaneous breaking of supersymmetry, which is supposed to occur in supersymmetric field theories. Now consider a one-particle quantum mechanical system in one dimension.

Infinitely many versions of SU(∞)

We give an explicit example of - infinitely many - pairwise non isomorphic Lie algebras L Λ (Λ irrational) each of which is a limit of su( N) as N → ∞, in the sense that for each Λ there exists a sequence N i ( Λ) of natural numbers N 1 < N 2 < … < N i < … and basis T a ( N i ) of su( N i ), such that the corresponding structure constants ƒ abc(N i) converge to those of L Λ fo N i → ∞.

NUMERICAL REEXAMINATION OF SUPERSYMMETRIC AND NONSUPERSYMMETRIC SU(5)-LIKE GRAND UNIFIED MODELS

The significance of numerical analysis in both nonsupersymmetric and supersymmetric Grand Unified Theories is pointed out. The exact analytical and numerical analysis we present shows a need of larger corrections to the values of unifying parameters, i.e. sin 2 θw, Mx, τp than those often quoted in literature. When an unmodified nonsupersymmetric version of SU(5) is considered we show that numerical computation allows some of the models still to be experimentally admissible. The difference between analytical and numerical results for the supersymmetric SU(5) model is also stressed. In particular, corrections due to the mass threshold of additional generations or supersymmetric particles are calculated both analytically and numerically at the two-loop level. We found them far more important for the final values of sin 2 θw, Mx and τp than the effects of Higgs-Yukawa couplings between scalars and fermions.

NUMERICAL REEXAMINATION OF SU(5)-LIKE MODELS

Analytical and numerical reexamination of SU(5)-like grand unified models is presented. Although an unmodified version of SU(5) is considered, we show that numerical calculations allow some of the models still to be experimentally admissible. Values for sin2 θw, Mx and τp are corrected. It is especially shown that the above parameters depend on the mass spectrum of higher generations much more than Higgs-Yukawa couplings could affect them.

On-shell and conformal N = 4 supergravity in superspace

We discuss the superspace geometries which are necessary to describe on-shell O(4) and SU(4) supergravity. The relation of central charge field strengths to physical spin-zero fields is exhibited and a “new” O(4) theory is shown to exist. The version of SU(4) supergravity which uses an antisymmetric tensor gauge field is found to require modifications of ordinary superspace. Finally the Poincaré supergeometry which admits the conformal N = 4 supermultiplet is constructed. It is shown that consistency of the Bianchi identities implies the existence of dimension zero auxiliary fields which are components of a non-linear multiplet.

Broken SU(3) × SU(3) × SU(3) × SU(3) symmetry

We argue that the “Eightfold Way” version of SU(3) symmetry should be extended to a product of up to four separate and badly broken SU(3) groups, including the γ 5 type SU(3) symmetry. A hierarchy of subgroups (or subalgebras) are considered within this framework, and two candidates are found to be interesting in view of experimental evidence. Main features of the theory are: (1) the baryons belong to a nonet; (2) there is an octet of axial vector gauge mesons in addition to one or two octets of vector mesons; (3) pseudoscalar and scalar mesons exist as “incomplete” multiplets arising from spontaneous breakdown of symmetry.