Finite matrix models with continuous local gauge invariance

We construct a hamiltonian lattice gauge theory which possesses local SU (2) gauge invariance and yet is defined on a Hilbert space of 5-dimensional real vectors for every link. This construction does not allow for generalization to arbitrary SU(N), but a small variation of it can be generalized to an SU(N) × U(1) local gauge invariant model. The latter is solvable in simple gauge sectors leading to trivial spectra. We display these by studying a U(1) local gauge invariant model with similar characteristics.     

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).     

On the sign of the n-p mass difference in gauge models

We examine the sign of the n-p mass difference in some gauge models based on the SU(2) × U(1) × U(1) or SU(2)_L × SU(2)_R × U(1) group, and show that a few specific elements of the neutral-vector-meson mass matrix can determine the sign of Δm|_n?p. We also present an SU(2) × U(1) × U(1) model which can give the correct Δm|_n?p.     

Stability and decay of the Dirac vacuum in external gauge fields

We consider various gauge fields coupled to the free Dirac equation according to symmetry principles. The gauge fields are treated as classical, unquantized fields. Sufficiently strong time-independent fields may give rise to spontaneous particle creation and to the decay of the symmetric Dirac vacuum into a new ground state with broken symmetry. The vacuum stability of the Dirac field is studied for the cases of external electromagnetic (U(1)), gravitational (Poincaré group including torsion) and Yang-Mills (SU(2)) potentials.     

Dynamical symmetry breaking of extended gauge symmetries

We construct asymptotically free gauge theories exhibiting dynamical breaking of the left-right gauge group G(LR)=SU(3)(c) x SU(2)(L) x SU(2)(R) x U(1)(B-L), and its extension to the Pati-Salam gauge group G(422)=SU(4)(PS) x SU(2)(L) x SU(2)(R). The models incorporate technicolor for electroweak breaking, and extended technicolor for the breaking of G(LR) and G422 and the generation of fermion masses. They include a seesaw mechanism for neutrino masses, without a grand unified theory (GUT) scale. These models explain why G(LR) and G422 break to SU(3)(c) x SU(2)(L) x U(1)(Y), and why this takes place at a scale (approximately 10(3) TeV) large compared to the electroweak scale, but much smaller than a GUT scale.     

Variational method in hamiltonian lattice gauge theories

A general expression for the expectation value of the hamiltonian of a d + 1 dimensional lattice gauge theory as a function of the norm of the variational state (that itself has the form of a partition function of a d-dimensional lattice gauge theory) is given. Applications include U(1), SU(2), U(2) and U(N) gauge theories for large N in d = 2 + 1 dimensions. It is also demonstrated that the deconfining phase transition is of first order in every dimension above the critical one, provided it is of first or second order at the critical dimension.     

Topology of quantum gauge fields and duality (I): Yang-Mills-Higgs system in 2 + 1 dimensions

The basic role of the representation of the gauge group in characterizing the topological excitations of the vacuum is pointed out. For SU(N) gauge fields on a lattice, the topological excitations are monopoles in the adjoint representation of the dual group ¹SU(N). This leads to a dual representation of the Yang-Mills-Higgs system in 2 + 1 dimensions. For SU(3) the deal theory in a scalar theory with discrete Weyl symmetry S₃. In the presence of adjoint Higgs fields the Weyl symmetry is broken in the Higgs phase but restored by pseudo-particles in the confinement phase.     

The small-volume expansion of gauge theories coupled to massless fermions

The small-volume expansion of the low-lying glueball states for SU(2) and SU(3) gauge theory, coupled to massless fermions with periodic and antiperiodic boundary conditions, is determined. For SU(3) with periodic boundary conditions the vacuum is eightfold degenerate and breaks part of the cubic group spontaneously. In all cases the scalar-to-tensor mass ratio m_A1⁺⁺/m_E⁺⁺ is 1.1 to 1.3 as in the pure-gauge case. We also discuss chiral symmetry.     

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.     

Chiral anomalies and constraints on the gauge group in higher-dimensional supersymmetric Yang-Mills theories

Chiral anomalies for gauge theories in any even dimension are computed and the results applied to supersymmetric theories in D = 6, 8 and 10. For D = 8 there is an anomalous chiral U(1) invariance, just as in D = 4, except for certain special groups. For D = 6 and D = 10 there is no anomalous chiral U(1) symmetry, but the gauge current is anomalous except for certain “anomaly-free” groups. For D = 6 the group is thereby constrained to be one of {SU(2), SU(3), exceptional}, while for D = 10 it is constrained to be one of {SU(n) n ≤ 5, USp(4), E₈}.     

Nonabelian electric and magnetic flux in unified SU(5) gauge theory

We study the long-distance behaviour of pure unified SU(5) gauge theory in the limit when the electroweak subgroup is unbroken. We show that the symmetry breaking pattern SU(5)→SU(3)_c×SU(2)×U(1)_Y, with SU(3)_c and SU(2) ×U(1)_Y realized, respectively, in confining and coulombic phases, is a possible dynamical phase of the SU(5) theory. The proof relies on showing that the duality equation of 't Hooft, relating the electric and magnetic flux, is exactly satisfied for the above symmetry breaking pattern. The infrared structure of SU(5), broken down to SU(3)_c×SU(2)×U(1)_Y, is not self-dual.     

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.     

Strong coupling expansions for the mass gap in lattice gauge theories

We derive strong coupling expansions for the mass gap in euclidean lattice gauge theories in any space-time dimension. For gauge groups SU(2), SU(3), Z₂ and Z₃ the series are calculated up to order g^?16. They are used to get rough estimates for the lowest glueball mass in continuum SU(2) and SU(3) gauge theories, assuming a sudden crossover from strong to weak coupling behaviour in the lattice theory.     

SU(2) ⊗ U(1) gauge theories of the generalized σ model for π0, η, η' → γγ decays

By embedding the chiral current-mixing gauge theories in the SU(2)_L ? SU(2)_R generalized σ model, it is shown that the correct sign and magnitude for π⁰ → γγ decay, as well as the SU(3) relation of π⁰, η, η' → γγ decays can be obtained within the framework of SU(2) ? U(1) gauge theories of weak and electromagnetic interactions.     

Hidden local gauge invariance in integrable magnetic chains

It is shown that local gauge transformations preserve the integrability of one-dimensional quantum Heisenberg chains. Abelian U(1) gauge transformations associated to z-rotations appear in the XXZ model which is worked out in detail. The exact energy spectrum derived by the Bethe ansatz turns out to be gauge-invariant whereas the eigenvectors are explicitly gauge-dependent. Isotropic XXX chains exhibit SU(2) ⊗ Z₂ gauge invariance properties and anisotropic XYZ chains possess discrete Z₂ ⊗ Z₂ gauge invariance.     

Neutral-current constraints on gauge models of weak and electromagnetic interactions

Sehgal and Hung and Sakurai have recently argued that neutrino-hadron neutral-current couplings must lie in one of two allowed regions in coupling-parameter space. We study this conjecture using realistic BNL ν_μ and ν̄_μ spectra in the elastic ν_μp (ν̄_μp) calculations and also study constraints imposed by theq²-distributions. On comparing to gauge models, we find that the Weinberg-Salam and SU(2)_L×SU(2)_R×U(1) models fall within one allowed region, while a vectorlike SU(3)×U(1) model and a hybrid SU(2)×U(1) model with a (u, b)_R doublet fall in the other region.     

Exact consequences of universality in SU(2) × U(1) gauge models

Exact consequences of universality within SU(2) × U(1) gauge models, with leptons in doublets and singlets, and for arbitrary vacuum expectation values of the Higgs fields, imply an extended Weinberg-Salam structure for leptons, with all neutrinos massless (the inverse statement is obvious). We also discuss approximate universality.     

The supersymmetric Wess-Zumino action and U(1) gauge fields

The supersymmetric effective action is constructed which when varied under gauge groups containing explicit U(1) factors reproduces the mixed gauge field contribution to the SU(N) anomaly while being U(1) invariant. It constitutes generalization of the supersymmetric Wess-Zumino action. The form of supersymmetric mixed anomaly is also discussed.     

Two-loop free energy for finite temperatureSU(3) gauge theory in a constant external field

A two-loop calculation of the free energy for finite temperatureSU(3) gauge theory in an external fieldA ₀=const is carried out using background Feynman gauge. Nontrivial minima of the free energy are obtained atA ₀{gT forg→0 corresponding to the gauge symmetry breakingSU(3)→U(1)×U(1). Higher order perturbative effects are briefly discussed.     

Systematic study of horizontal gauge theories

We analyze all the possible continuous horizontal gauge groups G _H in relation with their possibility to explain m _b ? m _t. We assume that the only effective fermionic degrees of freedom correspond to the known fermions but allow the possibility of adding a right handed neutrino to each family. We assume that the Higgs fields which generate masses for these fermions, trough renormalizable Yukawa couplings, transform as an irreducible representation of SU(3)_c ? SU(2)_L ? U(1)_Y ? G_H. Under these assumptions we find two U(1)_H or U(1) _H1 ? U(1) _H2 models free of anomalies and able to guarantee that only the top has a renormalizable mass-generating Yukawa coupling.