强相互作用系统的对称性及其破缺

本文简要介绍对称性及其破缺的概念和基本的数学上所说的幺正对称性等的微观粒子实现,从而为利用抽象的数学描述物理问题奠定基础。本文还简要介绍早期宇宙强相互作用物质演化过程的对称性及其破缺,尤其是可见物质质量的产生(比如DCSB)以及强相互作用等基本相互作用的规范对称性和破缺,为有意向探讨早期宇宙强相互作用物质演化的青年学者和研究生提供必要的知识储备,并打开一扇窗口。同时,还简要讨论原子核的对称性及其破缺,尤其是作为强相互作用多体系统的束缚态研究中的基本理论方法、(多粒子)壳模型及相互作用玻色子近似模型(IBM)、集体运动的描述及集体运动模式演化(形状相变)的研究方法及进展简况,提供一些在基本理论方法与前沿研究课题之间建立桥梁的实例。     

Classification of symmetry breaking by Wilson lines on the Z orbifold

We give a complete classification of gauge symmetry breaking by Wilson lines on the standard Z orbifold by deriving the general formula of the conditions of modular invariance and group invariance in the presence of background gauge fields. All possible E₆×SU(3) breaking in terms of one Wilson line is given. The symmetries of the electroweak and grand unification are obtained by combining two Wilson lines.     

Supersymmetric model with an extra U(1) gauge symmetry forbidding proton decay

In the standard model the proton is protected from decay naturally by gauge symmetries, whereas in the ordinary minimal supersymmetric standard model an ad hoc discrete symmetry is imposed for the proton stability. We present a new supersymmetric model in which the proton decay is forbidden by an extra U(1) gauge symmetry. Particle contents are necessarily increased to be free from anomalies, incorporating right-handed neutrinos. Both Dirac and Majorana masses are generated for neutrinos, yielding nonvanishing but small masses. The superpotential consists only of trilinear couplings and the mass parameter &mgr; of the minimal model is induced by spontaneous breaking of the U(1) symmetry.     

Prospects of experimentally reachable beyond Standard Model physics in inverse see-saw motivated <Emphasis Type="Italic">SO</Emphasis>(10) GUT

The grand unification theories based on SO(10) gauge group have been at the centre of attraction to beyond Standard Model phenomenology. The SO(10) gauge symmetry may pass through several intermediate symmetries before breaking to Standard Model. Therefore some higher symmetries may occur at the experimentally reachable scales. This feature flourishes easily in non-supersymmetric models compared to supersymmetric ones. We find that certain breaking chains give tremendous predictions for the physics being explored at various particle physics experiments. Explanation to neutrino masses through TeV scale inverse see-saw is the driving theme of the models studied.     

Gauge hierarchies of SU(N) grand unification

The structure of spontaneous breaking of SU(N) gauge symmetry for grand unification is investigated. The results obtained are applied to the analysis of SU(8) symmetry for which possible ways of breaking and intermediate symmetries are considered. It is assumed that the SU(8) group unifies the subgroups of colour, standard electroweak and horizontal symmetries. We find conditions which it is necessary to impose on the vacuum expectation values of Higgs multiplets to provide an arbitrary breaking pattern of SU(N) symmetry and conserve any intermediate symmetry. If in the SU(8) models considered fermions and mirror fermions do not violate the (V-A) and (V+A) structure of weak interactions, then their masses should not be greater than ～10² GeV. It is also shown that the contributions of fermion and Higgs multiplets to the renormalization group equation for the coupling constant of any subgroup of SU(N) are identical. Renormalization group identities for the case of arbitrary SU(N) breaking are given where the contribution of Higgs multiplets have been taken into account (but they cancel each other). Using these identities one can calculate the mass values for the breaking of the intermediate symmetries in the SU(8) models, and also exclude part of the possible breaking patterns.     

Tracking gauge symmetry factorizability on intervals

We track the gauge symmetry breaking pattern by boundary conditions on fifth and higher-dimensional intervals. It is found that, with Dirichlet–Neumann boundary conditions, the Kaluza–Klein decomposition in five-dimension for arbitrary gauge group can always be factorized into that for separate subsets of at most two gauge symmetries, and so is completely solvable. Accordingly, we present a simple and systematic geometric method to unambiguously identify the gauge breaking/mixing content by general set of Dirichlet–Neumann boundary conditions. We then formulate a limit theorem on gauge symmetry factorizability to recapitulate this interesting feature. Albeit the breaking/mixing, a particularly simple check of orthogonality and normalization of fields' modes in effective 4-dim picture is explicitly obtained. An interesting chained-mixing of gauge symmetries in higher dimensions by Dirichlet–Neumann boundary conditions is also explicitly constructed. This study has direct applications to higgsless/GUT model building.     

Discrete gauge symmetry anomalies

It has been recently argued that quantum gravity effects strongly violate all non-gauge symmetries. This would suggest that all low energy discrete symmetries should be gauge symmetries, either continuous or discrete. Acceptable continuous gauge symmetries are constrained by the condition they should be anomaly free. We show here that any discrete gauge symmetry should also obey certain “discrete anomaly cancellation” conditions. These conditions strongly constrains the massles fermion content of the theory and follow from the “parent” cancellation of the usual continuous gauge anomalies. They have interesting applications in model building. As an example we consider the constraints on the Z_N “generalized matter parities” of the supersymmetric standard model. We show that only a few (including the standard R-parity) are “discrete anomaly free” unless the fermion content of the minimal supersymmetric standard model is enlarged.     

Gauge symmetry breaking in matrix models

We argue that some features of the standard model, in particular the fermion assignment and symmetry breaking, can be obtained in matrix model which describes noncommutative gauge theory as well as gravity in an emergent way. The mechanism is based on the presence of some extra (matrix) dimensions. These extra dimensions are different from the usual ones which give to a noncommutative geometry of the Grönewold-Moyal type, and are reminiscent of the Connes-Lott model, although the action is very different.     

No role for muons in the DAMA annual modulation results

We construct the non-linear realized Lagrangian for the Goldstone bosons associated to the breaking pattern of SU(4) to SO(4). This pattern is expected to occur in any Technicolor extension of the standard model featuring two Dirac fermions transforming according to real representations of the underlying gauge group. We concentrate on the Minimal Walking Technicolor quantum number assignments with respect to the standard model symmetries. We demonstrate that for, any choice of the quantum numbers, consistent with gauge and Witten anomalies the spectrum of the pseudo Goldstone Bosons contains electrically doubly charged states which can be discovered at the Large Hadron Collider.     

Lie algebroid morphisms, Poisson sigma models, and off-shell closed gauge symmetries

Chern–Simons (CS) gauge theories in three dimensions and the Poisson sigma model (PSM) in two dimensions are examples of the same theory, if their field equations are interpreted as morphisms of Lie algebroids and their symmetries (on-shell) as homotopies of such morphisms. We point out that the (off-shell) gauge symmetries of the PSM in the literature are not globally well defined for non-parallelizable Poisson manifolds and propose a covariant definition of the off-shell gauge symmetries as left action of some finite-dimensional Lie algebroid.

Our approach allows us to avoid complications arising in the infinite-dimensional super-geometry of the BV- and AKSZ-formalism. This preprint is a starting point in a series of papers meant to introduce Yang–Mills type gauge theories of Lie algebroids, which include the standard YM theory, gerbes, and the PSM.     

Electric dipole moments in the generic supersymmetric standard model

The generic supersymmetric standard model is a model built from a supersymmetrized standard model field spectrum and the gauge symmetries only. The popular minimal supersymmetric standard model differs from the generic version in having R parity imposed by hand. We review an efficient formulation of the model and some of the recently obtained interesting phenomenological features, focusing on one-loop contributions to fermion electric dipole moments.     

Scalar lattice gauge theory

Scalar lattice gauge theories are models for scalar fields with local gauge symmetries. No fundamental gauge fields, or link variables in a lattice regularization, are introduced. The latter rather emerge as collective excitations composed from scalars. For suitable parameters scalar lattice gauge theories lead to confinement, with all continuum observables identical to usual lattice gauge theories. These models or their fermionic counterpart may be helpful for a realization of gauge theories by ultracold atoms. We conclude that the gauge bosons of the standard model of particle physics can arise as collective fields within models formulated for other “fundamental” degrees of freedom.     

Flat directions,string compactification and three generation models

We show how identification of absolutely flat directions allows the construction of a new class of compactified string theories with reduced gauge symmetry that may or may not be continuously connected to the original theory. We use this technique to construct a class of three generation models with just the Standard Model gauge group after compactification. We discuss the low-energy symmetries necessary for a phenomenologically viable low-energy model and construct an example in which these symmetries are identified with string symmetries which remain unbroken down to the supersymmetry breaking scale. Remarkably the same symmetry responsible for stabilising the nucleon is also responsible for ensuring one and only one pair of Higgs doublets is kept light. We show how the string symmetries also lead to textures in the quark and lepton mass matrices which can explain the hierarchy of fermion masses and mixing angles.     

Bott periodicity and realizations of chiral symmetry in arbitrary dimensions

We compute the chiral symmetries of the Lagrangian for confining “vector-like” gauge theories with massless fermions in d-dimensional Minkowski space and, under a few reasonable assumptions, determine the form of the quadratic fermion condensates which arise through spontaneous breaking of these symmetries. We find that for each type (complex, real, or pseudoreal) of representation of the gauge group carried by the fermions, the chiral symmetries of the Lagrangian, as well as the residual symmetries after dynamical breaking, exactly follow the pattern of Bott periodicity as the dimension changes. The consequences of this for the topological features of the low-energy effective theory are considered.     

Stabilizing the axion by discrete gauge symmetries

The axion solution to the strong CP problem makes use of a global Peccei–Quinn U(1) symmetry which is susceptible to violations from quantum gravitational effects. We show how discrete gauge symmetries can protect the axion from such violations. PQ symmetry emerges as an approximate global symmetry from discrete gauge symmetries. Simple models based on Z_N symmetries with N=11,12, etc., are presented realizing the DFSZ axion and the KSVZ axion. The discrete gauge anomalies are canceled by a discrete version of the Green–Schwarz mechanism. In the supersymmetric extension our models provide a natural link between the SUSY breaking scale, the axion scale, and the SUSY-preserving μ term.     

Existence of a nicolai mapping for some supersymmetry gauge theories

We find two classes of supersymmetry theories such that after Fermi-field integration and Bose-field transformation the graded partition function reduces to that of a free theory. We study theories with or without gauge symmetries and relate these results with the possibility of dynamical breaking of supersymmetry. Within these theories are N=2 and N=4 Super Yang-Mills.     

Complex CKM from spontaneous CP violation without flavor changing neutral current

We analyse the general constraints on unified gauge models with spontaneous CP breaking that satisfy the conditions that (i) CP violation in the quark sector is described by a realistic complex CKM matrix, and (ii) there is no significant flavor changing neutral current effects in the quark sector. We show that the crucial requirement in order to conform to the above conditions is that spontaneous CP breaking occurs at a very high scale by complex vevs of standard model singlet Higgs fields. Two classes of models are found, one consisting of pure Higgs extensions and the other one involving fermionic extensions of the standard model. We give examples of each class and discuss their possible embeddings into higher unified theories. One of the models has the interesting property that spontaneous CP violation is triggered by spontaneous P violation, thereby linking the scale of CP violation to the seesaw scale for neutrino masses.     

Invariance analysis and conservation laws of the wave equation on Vaidya manifolds

In this paper we discuss symmetries of classes of wave equations that arise as a consequence of some Vaidya metrics. We show how the wave equation is altered by the underlying geometry. In particular, a range of consequences on the form of the wave equation, the symmetries and number of conservation laws, inter alia, are altered by the manifold on which the model wave rests. We find Lie and Noether point symmetries of the corresponding wave equations and give some reductions. Some interesting physical conclusions relating to conservation laws such as energy, linear and angular momenta are also determined. We also present some interesting comparisons with the standard wave equations on a flat geometry. Finally, we pursue the existence of higher-order variational symmetries of equations on nonflat manifolds.     

Aspects of the super-unification of strong,electroweak and gravitational interactions

We develop a strategy for extracting low-energy phenomenological four-dimensional physics from the superstring. We discuss supersymmetry and gauge symmetry breaking, emphasizing key ingredients in the construction of a realistic model based on Calabi-Yau compactification. The incorporation of a no-scale mechanism for the dynamical generation of the electroweak gauge hierarchy imposes a unique choice of the gauge group SU(3) × SU(2) × U(1)², an almost unique set of matter fields and of Yukawa couplings. Our phenomenological analysis of this model includes the derivation of bounds on the mass of the new neutral gauge boson from the Z⁰ boson mass, low-energy neutral currents, and cosmology. We calculate the ratios of sparticle masses and give estimates of their magnitudes. These are based on detailed dynamical calculations demonstrating the feasibility of weak gauge symmetry breaking, made possible by radiative corrections to supersymmetry breaking initiated by a gaugino mass.     

Signals of the degenerate BESS model at the LHC

We discuss the possible signals of the degenerate BESS model at the LHC. This model describes a strongly interacting scenario responsible of the spontaneous breaking of the electroweak symmetry. It predicts two triplets of extra gauge bosons which are almost degenerate in mass. Due to this feature, the model has the property of decoupling and therefore, at low energies (below or of the order of 100 GeV) it is nearly indistinguishable from the Standard Model. However the new resonances, both neutral and charged, should give quite spectacular signals at the LHC, where the c.o.m. energy will allow to produce these gauge bosons directly. Received: 11 July 2000 / Published online: 13 November 2000