Construction of the effective Lagrangian of pionic processes for arbitrary SU(2)×SU(2) breaking

By assuming that SU(2)×SU(2) symmetry is broken by the isoscalar element of the representation (l, l), effective Lagrangians reproducing the results of current algebra and the PCAC assumption can be constructed by a direct method suggested byR. Dashen andM. Weinstein. The symmetry-breaking parts of these Lagrangians are the solutions (in closed form) of the differential equation for the breaking parts in Weinberg’s formalism.

     

An extended technicolour model for grand unification

An extended technicolour grand unification model based on the gauge groupE ₆×SU(7) extended technicolour is presented. The symmetry-breaking based on extended technicolour theory is discussed. It is shown that the existing phenomenology is well explained by the model. The strangeness changing neutral currents may not be a problem with this model.     

Magnetic moments of baryons in higher symmetry schemes including charm

Relations among the magnetic moments of charmed and uncharmed baryons are derived in the framework of SU(4) and SU(8) symmetries. The SU(3) resultμ (Σ ^o)=−μ(Λ) is not present in SU(4), but is obtained in SU(8). Higher order effects are further considered to improve the situation.     

Flavour symmetry breaking in quark vacuum condensates

We study SU(3) and SU(2) flavour symmetry violations in the vacuum from the viewpoint of nonperturbative quark mass generation and independently from charge symmetry-breaking considerations. The results for the ratios of quark condensates of different flavours are compatible with those of QCD sum rules. However, we find that very large SU(3) violating effects, suggested by some sum rule analyses, are barely accommodated in the present nonperturbative approach.     

Charm changing weak decays 1/2+ → 3/2+ + 0−/γ in SU(4) and SU(8) w

Weak decay modes (1/2⁺ → 3/2⁺ + 0⁻/γ) of charmed baryons are studied. Relations among the various decay amplitudes are derived in isospin, SU(3), SU(4) and SU(8) _w symmetries. Sextet dominance in SU(3) forbidsB(3) →D(10) +P(3*) decays. 20″ dominance in SU(4) specifies all the decays in terms of Θ⁻ decays. Weak decays of Θ* ₃ ⁺⁺ and Θ⁻ are also discussed. SU(8) _w symmetry predictsα , which is consistent with the experimental value.     

Gravity-induced weak symmetry breaking and supergravity

We give here a review of the recent developments of grand unified theories based onN=1 supergravity. We start with a brief introduction of supersymmetry and supergravity multiplets, and then discuss the construction of an invariant Lagrangian. The phenomena of gravity-induced weak symmetry breaking via the super Higgs effect at the tree level, corresponding to the conventional SU(5) gauge group, are then considered. We then extend this idea to the larger group SO(10), showing two possible breaking chains given as (i) SO(10)×susy→SU(2) _L ×U(1) _R ×U(1) _B-L ×SU(3) _C (≡ G₂₁₁₃)×susy→U(1)_em×SU(3) _C (G _LE ) predicting a secondZ-boson having mass lower than 1 TeV, and (ii) SO(10)×susy→SU(2) _L ×SU(2) _R ×SU(4)→(≡G₂₂₄)×susy→ SU(2) _L ×U(1) _Y ×SU(3) _C (≡ G₂₁₃)×susy→U(1)_em×SU(3) _C . We also consider the radiative breaking of weak symmetry via renormalisation group effects, which predicts the top quark mass. Some experimental signatures of the supersymmetric particles are investigated and possible future outlook is discussed. Invited talk presented at the International Symposium on Theoretical Physics, Bangalore, November 1984.     

Super-Landau models: Unitarity and hidden symmetries

We review a recent progress in constructing and studying superextensions of the Landau problem of a quantum particle moving on the two-sphere S ². These are the superspherical and superflag Landau models describing a nonrelativistic particle on the supermanifolds SU(2|1)/U(1|1) and SU(2|1)/[U(1) x U(1)]. Though in both models, under the “naive” definition of the inner product, there are negative-norm states, all norms can be made positive-definite by introducing a nontrivial “metric” in the space of states. So both models are unitary. The superflag model is shown to be quantum-equivalent to the supersphere model for the special choice of the intrinsic parameters. We also address the planar limit of the superspherical model, in which there arises the hidden world-line N =2 supersymmetry. An analog of this phenomenon in the superflag model is a dynamical enhancement of its SU(2|1) symmetry to SU(2|2).     

Some consequences of global horizontal symmetry

It is pointed out that the present SU(3) _c ×SU(2) _L ×U(1) gauge interactions with three families have a global horizontal symmetry (denoted hereby SU(3) _H ) which is broken only by the weak charged hadron currentJ _h. Also, with (u, c), (d, s), (v _e, {ie437-1}) and (e ⁻,μ ⁻) as doublets of SU(2) _H (subgroup of SU(3) _H ),J _h has simple transformation properties under this subgroup. Amplitude relations, using SU(2) _H symmetry, for hadronic leptonic and semileptonic decays are given.     

Adjoint representation admixture to weak nonleptonic decays in SU(4) and SU(8)

In order to remove some of the unsatisfactory features of the GIM model, we consider15-admixture in SU(4). ΔC=±ΔS decays remain unaffected. Lee-Sugawara sum-rule is obtained.15-admixture is extended then to63-admixture in SU(8). The most general Hamiltonian (H _w∼63⊕720⊕1232) in SU(8) is found to give Lee-Sugawara relation and Σ₊ ⁺=0 forS-wave decays of uncharmed baryons. Decay amplitude relations for ΔC=−1, ΔS=0 mode are obtained.     

基于阿贝尔黑格斯变量的杨-米尔斯理论的红外阿贝尔化

通过SU(2)规范场的法捷耶夫-Niemi分解给出了有效阿贝尔-黑格斯型作用量的 一个计算方法. 具体指出了该分解中所用的自然规范固定以及阿贝尔投射与杨-米尔斯理论的红外动力学之间的内在关系. 推导出了色电场的一个伦敦型方程.     

Non-leptonic weak decays of charmed baryons

It is shown that the ΔC _h=ΔS decays of a baryon sextuplet, triplet and singlet of SU (3), into meson and baryon, can provide simple tests of the iscspin and SU (3) transformation properties of the ΔC _h=ΔS non-leptonic interaction in the Glashow Iliopoulos-Maiani scheme.     

Supersymmetric preon models with three-fermion generations

A class of supersymmetric preon models is considered in which the hypercolour groupG _HC and the unbroken flavour groupG _f anomalies are zero without needing spectators. It is shown that forG _HC=SU(2) and SU(3) quarks and leptons as composites can be obtained satisfying ’t Hooft’s anomaly matching conditions. For the case ofG _HC=SU(3),G _f can accommodate a horizontal symmetry group to describe just three generations.     

A note about the t’Hooft ansatz for SU(N) real-time gauge theories

The t’Hooft ansatz, which reduces the classical Yang-Mills theory to the λϕ⁴ one, is under consideration. It is shown that, in the framework of this ansatz, the real-time classical solutions for the arbitrary SU(N) gauge group are obtained by embedding SU(2) × SU(2) into SU(N). It is argued that this group structure is the only possibility in the framework of the considered ansatz. New explicit solutions for SU(3) and SU(5) gauge groups are shown. The text was submitted by the authors in English.     

On bilocal gauge field theory

The nonlocal gauge group of unitary integral operators U _n (∞) is considered. Gluons in the nonlocal version of QCD are described by the bilocal gauge fields (BGF). The Higgs effect for BGF are discussed. It is shown that the local SU(n) gauge theory can be treated as a local limit of spontaneously broken U _n(∞)/SU(n) BGF theory.     

On the Quantum Invariants for the Spherical Seifert Manifolds

We study the Witten–Reshetikhin–Turaev SU(2) invariant for the Seifert manifolds S ³/Gamma where Γ is a finite subgroup of SU(2). We show that the WRT invariants can be written in terms of the Eichler integral of modular forms with half-integral weight, and we give an exact asymptotic expansion of the invariants by use of the nearly modular property of the Eichler integral. We further discuss that those modular forms have a direct connection with the polyhedral group by showing that the invariant polynomials of modular forms satisfy the polyhedral equations associated to Γ.     

Is U(1) H a good family symmetry?

We analyze U(1) _H as a horizontal symmetry and its possibilities to explain the known elementary-fermion masses. We find that only two candidates, in the context of SU(3) _c ⊗SU(2) _L ⊗U(1) _Y ⊗U(1) _H nonsupersymmetric, are able to fit the experimental resultm _b≪m _t.     

Pairing-plus-quadrupole model and nuclear deformation: A look at the spin-orbit interaction

The pairing-plus-quadrupole model, realized in the framework of the Elliott SU(3) scheme, is used to study the combined effects of the quadrupole-quadrupole, pairing, and spin-orbit interactions on ground state shapes of nuclear systems. Relevant measures for nuclear deformation are reviewed. Representation mixing induced by the symmetry-breaking pairing and spin-orbit forces is shown to soften the deformation. The angular momentum dependence of the results is discussed.     

Neutrino mixing and masses in a left–right model with mirror fermions

In the framework of a left–right model containing mirror fermions with gauge group SU(3) _C ⊗SU(2) _L ⊗SU(2) _R ⊗U(1) _Y′, we estimate the neutrino masses, which are found to be consistent with their experimental bounds and hierarchy. We evaluate the decay rates of the Lepton Flavor Violation (LFV) processes μ→eγ, τ→μγ and τ→eγ. We obtain upper limits for the flavor-changing branching ratios in agreement with their present experimental bounds. We also estimate the decay rates of heavy Majorana neutrinos in the channels N→W ^± l ^∓, N→Zν _l and N→Hν _l , which are roughly equal for large values of the heavy neutrino mass. Starting from the most general Majorana neutrino mass matrix, the smallness of active neutrino masses turns out from the interplay of the hierarchy of the involved scales and the double application of seesaw mechanism. An appropriate parameterization on the structure of the neutrino mass matrix imposing a symmetric mixing of electron neutrino with muon and tau neutrinos leads to tri-bimaximal mixing matrix for light neutrinos.     

The W N Minimal Model Classification

We first rigourously establish, for any N ≥ 2, that the toroidal modular invariant partition functions for the (not necessarily unitary) W _N (p, q) minimal models biject onto a well-defined subset of those of the SU(N) × SU(N) Wess-Zumino-Witten theories at level (p − N, q − N). This permits considerable simplifications to the proof of the Cappelli-Itzykson-Zuber classification of Virasoro minimal models. More important, we obtain from this the complete classification of all modular invariants for the W ₃(p, q) minimal models. All should be realised by rational conformal field theories. Previously, only those for the unitary models, i.e. W ₃(p, p + 1), were classified. For all N our correspondence yields for free an extensive list of W _N (p, q) modular invariants. The W ₃ modular invariants, like the Virasoro minimal models, all factorise into SU(3) modular invariants, but this fails in general for larger N. We also classify the SU(3) × SU(3) modular invariants, and find there a new infinite series of exceptionals.     

Chern-Simons solitons,Toda theories and the chiral model

The two-dimensional self-dual Chern-Simons equations are equivalent to the conditions for static, zero-energy solutions of the (2+1)-dimensional gauged nonlinear Schrödinger equation with Chern-Simons matter-gauge dynamics. In this paper we classify all finite chargeSU(N) solutions by first transforming the self-dual Chern-Simons equations into the two-dimensional chiral model (or harmonic map) equations, and then using the Uhlenbeck-Wood classification of harmonic maps into the unitary groups. This construction also leads to a new relationship between theSU(N) Toda andSU(N) chiral model solutions.This work is supported in part by funds provided by the U.S. Department of Energy (D.O.E.) under contract #DE-AC02-76ER03069, and NSF grant #87-08447