Random walk approximation in a chiral Yukawa-model and global symmetries

The fermion propagator is investigated in a chiral Yukawa-model with explicit mirror fermions applying the random walk approximation to the hopping parameter expansion. It is shown that the globalSU(2) _L ?SU(2) _R symmetry breaking due to the mass splitting within fermion doublets does influence the critical behaviour of the fermion spectrum in the continuum limit. In particular, in the case of a mirror pair of split doublets, whereSU(2) _L ⊕SU(2) _R is broken toSU(2) _L , no evidence is found for a dynamical spectrum doubling at infinitely strong bare Yukawa-couplings, in contrast to the case with degenerate doublets andSU(2) _L ?SU(2) _R symmetry.     

A Wilson-Yukawa Model with undoubled chiral fermions in 2D

We consider the fermion mass spectrum in the strong coupling vortex phase (VXS) of a lattice fermion-scalar model with a global U(1)_L × U(1)_R, in two dimensions, in the context of a recently proposed two-cutoff lattice formulation. The fermion doublers are made massive by a strong Wilson-Yukawa coupling, but in contrast with the standard formulation of these type of models, in which the light fermion spectrum was found to be vector-like, we find massless fermions with chiral quantum numbers at finite lattice spacing. When the global symmetry is gauged, this model is expected to give rise to a lattice chiral gauge theory.     

Variational study of vacuum structure with fermions ind+1 dimensional Hamiltonian lattice gauge theory

The physical vacuum state and general expression for the Hamiltonian ofd+1 dimensional lattice gauge theory are given by incorporating the exact ground state of pure gauge theory and the variational fermion vacuum state. The applications toSU(2) andSU(3) gauge theories in 2+1 and 3+1 dimensions are demonstrated and the fermion condensates \(\left\langle {\bar \psi \psi } \right\rangle \) as functions of 1/g ² are calculated.     

Natural fermion mass hierarchy and mixings in family unification

We present an SU(9)$\mathit{SU}(9)$ model of family unification with three light chiral families, and a natural hierarchy of charged fermion masses and mixings. The existence of singlet right handed neutrinos with masses about two orders of magnitude smaller than the GUT scale, as needed to understand the light neutrinos masses via the see-saw mechanism, is compelling in our model.     

On the fermion mass-spectrum of Kaluza-Klein supergravity

A general setup for the harmonic expansions of D = 11 supergravity about classical compactifying solutions is given. Mass-matrices for the fermion mass-spectrum are derived both in the case of Freund-Rubin backgrounds and of Englert type solutions. The mass-matrix is explicitly given in terms of the eigenvalues of invariant operators on the 7-manifold. In the Freund-Rubin case the mass formula is very easy, while in the Englert case it is quite complicated and requires special techniques. In the second part of the paper applications to special manifolds for the Freund-Rubin background are considered, postponing the application of the general Englert formula to future publications. In particular, the round 7-sphere with the complete fermion spectrum and the SU(3) × SU(2) × U(1) isometric M^pqr-spaces are considered. For this latter the condition for the existence of a spinor structure (p = odd number) is established, deriving the explicit spectrum and the mass-eigenvalues for one of the two sectors of which it is composed. This relies on a general distinction between longitudinal and transverse fermion particle-modes which is emphasized in the first part of the paper. In this paper the longitudinal spectrum of M^pqr cosets is derived, postponing the transverse one to future work.     

Spontaneous SU(2) symmetry violation in the SU(2) L × SU(2) R × SU(4) electroweak model

A new approach to electroweak (EW) composite scalars is developed starting from the fundamental gauge interaction on high scale. The latter is assumed to have the group structure SU(2) _L × SU(2) _R × SU(4), where SU(4) is the Pati-Salam color-lepton group. The topological EW vacuum filled by instantons is explicitly constructed and the resulting equations for fermion masses exhibit spontaneous SU(2) flavor symmetry violation with possibility of very large mass ratios.     

Gauge theory ofSU(2) Weyl fermion: Is it consistent?

Gauge theory ofSU(2) Weyl fermions was alleged by Witten to be inconsistent due to global anomaly. Evidences of inconsistency were also reported from contradictions between the anomalousU(1) symmetry and the fact that theSU(2) group is free of local anomaly. Here we show how the zero modes of Dirac operator, ignored by the authors of these arguments, play a decisive role and saveSU(2) Weyl fermions from inconsistency in each case. The symmetric chiral current, obtained by adding the Chern-Simons current to the fermionic chiral current, fails to be conserved precisely due to the contributions of zero modes to the ABJ anomaly equation. The Jacobian of the fermion measure under rigid chiralU(1) transformation is, however, guaranteed to be trivial by the Atiyah-Singer index theorem. Finally, a zero mode is the point of bifurcation of eigenvalue trajectory in the homotopy space. In its neighbourhood the hypothesis of adiabaticity made by Witten breaks down due to violent oscillations between levels, which makes his allegation of global anomaly untenable.     

Two dimensional gases of weight charges and SU(N) fermino theories

We analyze two dimensional gases composed of particles interacting via a Coulomb or Yakawa potential through their “non-Abelian” charges. These charges are taken to be elementary weight or root vectors of SU(N). The grand partition function of these gases is shown to be equivalent to the generating functional of sine-Gordon models with weight vectors and hence to that of SU(N) fermion models. The fermion field creates or annihilates topological solitons which have elementary weight vectors as topological quantum numbers. Then, we discuss the confinement of fermions in the SU(N) Higgs models, where instantons (Z_N vortices) constitute a Yukawa gas of weight charges. We prove that fermions are confirmed by the effects of instantons in the SU(N) Higgs models in contrast with the Abelian Higgs model.     

Unification,KK-thresholds and the top Yukawa coupling in F-theory GUTs

In a class of F-theory SU(5) GUTs the low energy chiral mass spectrum is obtained from rank one fermion mass textures with a hierarchical structure organized by U(1) symmetries embedded in the exceptional E ₈ group. In these theories chiral fields reside on matter ‘curves’ and the tree-level masses are computed from integrals of overlapping wave functions of the particles at the triple intersection points. This calculation requires knowledge of the exact form of the wave functions. In this work we propose a way to obtain a reliable estimate of the various quantities which determine the strength of the Yukawa couplings. We use previous analysis of KK-threshold effects to determine the (ratios of) heavy mass scales of the theory which are involved in the normalization of the wave functions. We consider similar effects from the chiral spectrum of these models and discuss possible constraints on the emerging matter content. In this approach, we find that the Yukawa couplings can be determined solely from the U(1) charges of the states in the ‘intersection’ and the torsion which is a topological invariant quantity. We apply the results to a viable SU(5) model with minimal spectrum which satisfies all the constraints imposed by our analysis. We use renormalization group analysis to estimate the top and bottom masses and find that they are in agreement with the experimental values.     

Dynamical fermion mass hierarchy and flavour mixing

The chiral symmetry breaking of high colour representations produces dynamical breaking of the standard electroweak gauge symmetry. By enlarging the colour group and subsequently breaking it down toSU(3) _c fermions acquire radiative masses from the chiral breaking. We present attempts to produce realistic fermion mass matrix in two classes of models depending on the way that the colour group is enlarged. A realistic example is found in one of these classes of models.     

Axion depending on the Higgs sector inSU(2)L×SU(2)R×U(1)

Using Higgses with quantum numbers of fermion bilinears we discuss the axion in four different Higgs sectors inSU(2)_L×SU(2)_R×U(1). Three of the cases are similar to the “standard axion” in the Salam-Weinberg model and in one case the axion can be made invisible.     

AnSU(2)l ⊗SU(2)r symmetric Yukawa model in the symmetric phase

The lattice regularizedSU(2)l ?SU(2)r symmetric scalar fermion model with explicit mirror fermions is investigated in the phase with unbroken symmetry. In the present work numerical Monte Carlo calculations with dynamical fermions are performed on 4³·8 and 4³·16 lattices near the expected perturbative Gaussian fixed point. The bare Yukawa coupling of the mirror fermion is fixed at zero. Global symmetries of the model are discussed, and the numerical results are supported by lattice perturbation theory.     

From chiral to two-dimensional Wess-Zumino-Novikov-Witten model via quantum gauge group

We study the canonical quantization of the SU(n) WZNW model. Decoupling the chiral dynamics requires an extended state space including left and right monodromies as independent variables. In the simplest (n = 2) case we explicitly show that the zero modes of the monodromy extended SU(2) WZNW model give rise to a quantum group gauge theory in a finite-dimensional Fock space. We define the subspace of U_q(sl(2)) ⊗ U_q(sl(2))-invariant vectors on which the monodromy invariance is also restored and construct the physical space applying a generalized cohomology condition.     

Integrable string models of WZNW model type with constant SU(2), SO(3), SP(2) and SU(3) torsion and hydrodynamic chains

The integrability of string model of WZNW model type with constant SU(2), SO(3), SP(2) torsion is investigated. The closed boson string model in the background gravity and antisymmetric B-field is considered as integrable system in terms of initial chiral currents. The model is considered under assumption that internal torsion related with metric of Riemann-Cartan space and external torsion related with antisymmetric B-field are (anti)coincide. New equation of motion and exact solution this equation was obtained for string model with constant SU(2), SO(3), SP(2) torsion. New equations of motion and new Poisson brackets (PB) for infinite dimensional hydrodynamic chains was obtained for string model with constant SU(n), SO(n), SP(n) torsion for n → ∞.     

The construction of vector-like supersymmetric gauge models of weak and electromagnetic interactions

Despite great efforts and partial successes the situation with respect to spontaneously broken supersymmetric unified gauge models of weak, electromagnetic and strong interactions has remained quite unsatisfactory up to now. Starting from the most simple SU(2) × U(1) cases we exploit possible extensions. This naturally leads to a consideration of vector-like models with—in the first instance—a larger number of multiplets. Although the later can be made massive without spoiling the conservation of fermion number, the additional massive fermions only show parity conserving interactions with all the intermediate vector fields. Therefore models with larger gauge groups are considered: SU(2) × SU(2) × U(1) with two quartets, SU(3) × U(1) with four triplets, and finally SU(3) × SU(2) × U(1) with two sextets of matter fields. None of these can be accepted yet as a true model for physical particles, but it is shown how different negative features in the simple theories may be avoided in the more complicated ones. Thus our results may be considered as an encouraging starting point for investigations of larger gauge groups in supersymmetric models.     

Natural flavour conservation in the neutral currents and the determination of the Cabibbo angle

We point out a conflict between the requirement of natural flavour conservation in the neutral currents and the possibility of determining the generalized Cabibbo angles as a function of the quark masses in the SU(2) × U(1) and in the SU(2)_L × SU (2)_R × U (1) models. The general implications of natural flavour conservation in the neutral currents on the fermion mass matrices are also discussed.     

Unification of 3-3-1 models

A 3-3-1 model is constructed for three families that can be embedded into a single SU(8) unified model. Assuming appropriate branching rules and symmetry-breaking pattern, a complete fermion content is found within irreducible representations of SU(8), where light Standard Model fermions, heavy 3-3-1 fermions and superheavy fermions may be distinguished.     

The trinification model <Emphasis Type="Italic">SU</Emphasis>(3)<Superscript>3</Superscript> from orbifolds for fuzzy spheres

In this review, we consider an N = 4 supersymmetric SU(3N) gauge theory defined on the Minkowski spacetime. Then we apply an orbifold projection leading to an N = 1 supersymmetric SU(N)³ model, with a truncated particle spectrum. Then, we present the dynamical generation of (twisted) fuzzy spheres as vacuum solutions of the projected field theory, breaking the SU(N)³ spontaneously to a chiral effective theory with unbroken gauge group the trinification group, SU(3)³.