Attraction to large gauge orbits

SU(N) gauge systems are attracted to large orbits of the global gauge group by an invariant and calculable potential. In models the wave function becomes increasingly localized near the maximal orbit as N → ∞, which explains the success of semiclassical methods. Picturing the links U_i of the lattice as particles on an SU(N) group manifold, the effect favors large moments of inertia about U = 1. It thus opposes the magnetic interaction, and tends to destabilize the perturbative vacuum.     

Supercompositeness from superstrings

String Unified Models based on the k = 1 level of the Kac-Moody Algebra, predict the existence of “exotic” new states which carry fractional electric charges. We analyse the possibility of considering these “exotics” as preonic matter which can be used to form the families and the gauge group breaking higgs scalars. It is proposed that such a formation may occur provided that these states transform non-trivially under a non-Abelian gauge group with a relatively large rank in order to confine them at a sufficiently large scale. Such a situation is natural in string derived unified models, since the role of the confining group can be played by (part of) the Hidden symmetry. As an example, we present a string derived toy model based on the SU(4) × SU(2) _L × SU(2) _R Pati-Salam gauge group.     

Trimuons in SU(3) gauge models

We discuss models of weak interactions which can account for the recently observed μ^?μ^?μ⁺ events in v_μ reactions by allowing for the production of a new heavy neutral lepton and a new quark. One model is based on an SU(3) × U(1) gauge theory in shich the left-handed leptons are classified in anti-triplets. The second model catagorizes the leptons in an octet in accord with the more restrictive SU(3) weak gauge theory.     

Asymptotic freedom constraints on grand unified gauge theories

Constraints on the fermion and Higgs scalar content of grand unified gauge theories, imposed by the requirement of asymptotic freedom for the gauge couplings, are derived for models which have fermion representations with only color singlets and color triplets. The constraintn _f ≦16 on the numbern _f of flavors of color triplet quarks in pure QCD is removed. Definitive limits are placed on the representation content of theories based on the exceptional groups.     

Membrabe models and generalized Z2 gauge theories

We consider models of (d?n)-dimensional membranes fluctuating in a d-dimensional space under the action of surface tension. We investigate the renormalization properties of these models perturbatively and in $\text{1}\text{n}$ expansion. The potential relationships of these models to generalized Z₂ gauge theories are indicated.     

Pseudoscalar Higgs bosons at the LHC: production and decays into electroweak gauge bosons revisited

We analyse and compute, within a number of standard model (SM) extensions, the cross sections σ _A→VV′ for the production of a heavy neutral pseudoscalar Higgs-boson/spin-zero resonance at the LHC and its subsequent decays into electroweak gauge bosons. For comparison we calculate also the corresponding cross sections for a heavy scalar. The SM extensions we consider include a type-II two-Higgs doublet model (2HDM), a 2HDM with four chiral fermion generations, the minimal supersymmetric extension of the SM (MSSM), and top-colour assisted technicolour models. Presently available phenomenological constraints on the parameters of these models are taken into account. We find that, with the exception of the MSSM, these models permit the LHC cross sections σ _A→VV′ to be of observable size. That is, a pseudoscalar resonance may be observable, if it exists, at the LHC in its decays into electroweak gauge bosons, in particular in WW and γ γ final states.     

Dynamical supersymmetry breaking and gauge anomalies

Some aspects of supersymmetric gauge theories and discussed. It is shown that dynamical supersymmetry breaking does not occur in supersymmetric QED in higher dimensions. The cancellation of both local (perturbative) and global (non-perturbative) gauge anomalies are also discussed in supersymmetric gauge theories. We argue that there is no dynamical supersymmetry breaking in higher dimensions in any supersymmetric gauge theories free of gauge anomalies. It is also shown that for supersymmetric gauge theories in higher dimensions with a compact connected simple gauge group, when the local anomaly-free condition is satisfied, there can be at most a possibleZ ₂ global gauge anomaly in extended supersymmetricSO(10) (or spin (10)) gauge theories inD=10 dimensions containing additional Weyl fermions in a spinor representation ofSO(10) (or spin (10)). In four dimensions with local anomaly-free condition satisfied, the only possible global gauge anomalies in supersymmetric gauge theories areZ ₂ global gauge anomalies for extended supersymmetricSP(2N) (N=rank) gauge theories containing additional Weyl fermions in a representation ofSP(2N) with an odd 2nd-order Dynkin index.     

E6 as a unifying gauge symmetry

Some consequences of embedding gauge models of strong, weak and electromagnetic interactions in the exceptional group E₆ are presented.     

Mixing of leptonic number in a general SU(2)L ⊗ U(1) ⊗ SU(2)R model

We discuss a general leptonic model based on the SU(2)_L ? U(1) ? SU(2)_R gauge group and we present general results for the ? → ?′ γ and ν? → ν?′γ processes, which can be used for any model based on the SU(2)_L ? U(1) ? SU(2)_R gauge group or on any of its subgroups. The predictions of the μ → eγ branching ratio and of the neutrino lifetime for various models discussed in the literature are reviewed. The main results are summarized in tables.     

Grand unification of effective gauge theories

An effective non-renormalizable SU(3)×SU(2)×U(1) invariant gauge theory results at ordinary energies when superheavy fields are integrated out from a grand unified theory based on a simple gauge group G. The solutions of the second-order renormalization-group equations for the gauge coupling constants of the effective theory are examined. General formulae for the superheavy vector boson mass and for sin²θ near M_W are given in this approach to grand unification. The superheavy vector boson mass is plotted against the QCD scale parameter Λ for a certain set of grand unified models. Corrections to the prediction when the set of models is enlarged are discussed, and illustrated with examples from G≡SU(5) and O(10).     

Comments on a Minimal Quasiparticle Approach for the QGP and Its Large-N c Limits

A minimal quasiparticle approach for describing QGP at temperatures much higher than the critical one is discussed. It involves an ideal-gas framework in which quark and gluon masses depend on temperature. This model is able to reproduce the recent equations of state computed in lattice QCD for temperatures typically higher than 2 T _c , in a range in which it is reasonable to neglect interactions between quasiparticles. In addition, the equations of state for a generic gauge theory with gauge groups SU(N _c ) and quarks in an arbitrary representation are studied. The gauge independence in the pure glue sector and the large-N _c equivalence between the gauge groups SU(N _c ) and SO(2N _c ) in a full plasma is finally shown for normalized thermodynamic quantities.     

Low energy supergravity and the anomalous magnetic moment of the muon

The anomalous magnetic moment of the muon (g ? 2)_μ imposes constraints on the masses and mixings of spin-zero leptons, gauge fermions, and Higgs fermions in minimal models of low energy supergravity. We demonstrate that there exist only limited values of the parameters in these models that are ruled out by existing limits on (g ? 2)_μ.     

Deconfining and chiral phase transitions in quantum chromodynamics at finite temperature

We give further arguments to support the claim of Svetitsky and Yaffe that the finite-temperature transition in 4-dimensional SU(N) gauge theories is in the universality class of 3-dimensional Z_N spin models. We show that this implies a smoothing out of the transition when quarks are added to the system as long as N ≠ 3. For N = 3 the pure gauge transition is expected to be first order and will be smoothed by quarks only if the quark contribution to the internal energy is larger than the latent heat of transition.     

Fermion mass generation via Kaluza-Klein fermions under the influence of a gauge field within a (2 + 1)-dimensional model

We considered the generation of mass on a two-dimensional brane within a three-dimensional model with four-fermion interaction, including an external gauge field A ₃. In the scope of this model, the generated mass proves to be lighter than the masses of the Kaluza-Klein modes. This indicates the possibility of solving the mass hierarchy problem in realistic four-dimensional models. As well, the dependences of the effective potential and the constant of coupling on such characteristics of the model as the radius of compactification, gauge field, and phase-shift parameter were obtained.     

Spontaneous symmetry breakings in Z2 gauge theories for doped quantum dimer and eight-vertex models

Behavior of doped fermions in Z₂ gauge theories for the quantum dimer and eight-vertex models is studied. Fermions carry charge and spin degrees of freedom. In the confinement phase of the Z₂ gauge theories, these internal symmetries are spontaneously broken and a superconducting or Neél state appears. On the other hand in the deconfinement-topologically ordered state, all symmetries are respected. From the view point of the quantum dimer and eight-vertex models, this result indicates interplay of the phase structure of the doped fermions and background configuration of the dimer or the eight-vertex groundstate. At the quantum phase transitions in these systems, structure of the doped fermions groundstate and also that of the background dimer or eight-vertex groundstate both change. Translational symmetry breaking induces a superconducting or antiferromagnetic state of the doped fermions.     

Cosmological constraints on heavy weakly interacting fermions

The masses and lifetimes of very heavy weakly interacting fermions which appear in many grand unified gauge models are constrained by the requirement that their decays in the hot big bang early universe should not generate excessive entropy which would dilute n_B/n_γ below its observed value.     

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.     

Asymmetric orbifolds and higher level models

I introduce a class of string constructions based on asymmetric orbifolds leading to level two models. In particular, I derive in detail various models with gauge groups E₆ and SO(10), including a four generation E₆ model with two adjoint representations. The occurrence of multiple adjoint representations is a generic feature of the construction. In the course of describing this approach, I will address the problem of twist phases in higher twisted sectors of asymmetric orbifolds.     

Ghost-free non-Abelian gauge theory: renormalization and gauge-invariance

Although it has been known for a long time that the special case n^μA_μ = 0 for an axial gauge of a vector field A_μ, characterized by a direction n_μ, is free from the peculiar loop complications inherent in all other known gauges of non-Abelian gauge theories, practical use of this ghost-free gauge has often met with some reserve. The reasons were always difficulties in the development of the theoretical formalism, all of which can be traced back to a singularity at n^μp_μ = 0 where p is some four-momentum. This paper, which is a sequel to an earlier one by one of the authors, is intended to show that within the functional integration formalism a consistent field theory can be developed. Here we first prove the gauge invariance of the renormalized theory, allowing for the presence of an arbitrary number of scalar and fermion fields with spontaneous symmetry breaking. Then it is shown that all on-shell elements for the physical S-matrix between properly selected physical sources are independent of n_μ (gauge invariant) and so are the renormalized masses.