Non-planar diagrams in the large N limit of U(N) and SU(N) lattice gauge theories

It is shown that the limit as N → ∞ with g²N fixed of the strong coupling expansion for the vacuum expectation values of a U(N) or SU(N) lattice gauge theory is not given by a sum of planar diagrams. This contradicts a result claimed by De Wit and 't Hooft.     

Comparing O(N) and SU(N) × SU(N) spin systems in 1 + 1 dimensions to SU(N) gauge theories in 3 + 1 dimensions

We have computed the scale breaking Λ parameters of the euclidean and hamiltonian formulations of the lattice regulated O(N) and SU(N) × SU(N) spin systems in 1 + 1 dimensions in terms of the Λ_PV parameters of the Pauli-Villars regulated continuum models. Using lattice perturbation theory, the renormalized mass gap has been determined in terms of Λ_PV for each model. These results are compared to analogous calculations in SU(N) gauge theories.     

The phase structure of SU(N)/Z(N) lattice gauge theories

The phase structure of pure SU(N)/Z(N) lattice gauge theories in four dimensions is discussed. The presence of ZN monopoles plausibly leads to a phase transition. A Monte Carlo simulation of SO(3) shows the presence of a very strong, may be first order, phase transition.     

Towards a finite N = 2 susy GUT

We consider finite, N = 2 supersymmetric GUTs based on gauge groups SU(n) and SO(n). As an example, we discuss a semirealistic model based on SO(12). We argue that in finite, N = 2 supersymmetric GUTs, gauge symmetry breaking should occur dynamically. We present a heuristic picture in which this is induced by soft, finiteness preserving SUSY breaking terms. The bound states formed cause a very rapid evolution of the SO(12) coupling constant and break SO(12) into SU(4)×SU(3)_C×U(1).     

Transition from strong to weak coupling in SU(N) lattice gauge theories

A possible explanation is proposed for the crossover from strong to weak coupling region in SU(N) lattice gauge theories. We predict the pointswhere the crossover takes place for all SU(N)M: For example, g² ≈ 2.0 for SU(2), g² ≈ 1.0 for SU(3) and lim_N→∞Ng²(SU(N) ≈ 2.0.     

Improved mean field studies of SU(N) chiral models and comparison with numerical simulations

SU(N) × SU(N) matrix models are investigated using a systematic expansion around the classical mean field result. One-loop corrections for N = 2?5, and ∞ are computed for the two-, three-, and four-dimensional models. The results are in good agreement with numerical simulations of these models.     

All-loop group-theory constraints for color-ordered SU(N) gauge-theory amplitudes

We derive constraints on the color-ordered amplitudes of the L-loop four-point function in SU(N) gauge theories that arise solely from the structure of the gauge group. These constraints generalize well-known group theory relations, such as U(1) decoupling identities, to all loop orders.     

Nonconvergence of the 1/N expansion for SU(N) gauge fields on a lattice

We present specific examples that demonstrate the non-convergence of the 1/N expansion for the lattice theory of SU(N) gauge fields.     

Mean field and Monte Carlo studies of SU(N) chiral models in three dimensions

SU(N) chiral models defined on three-dimensional cubic lattices arestudied using mean field and Monte Carlo techniques. Mean field theory predicts first-order transitions for all finite N greater than two. The mean field estimates of the transition temperature and discontinuity of the order parameter are in good agreement with computer simulations for N = 3 and 4. The N → ∞ limit of mean field theory has a first-order phase transition.     

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.     

Linearized N = 2 superfield supergravity

We present the formulation of linearized SU(2) supergravity and U(2) conformal supergravity in terms of unconstrained N = 2 superfields: the gauge superfield, compensating superfields, gauge transformations, supertensors, actions and covariant derivatives.     

Duality for Z(N) gauge theories

The duality properties of simple Z(N) gauge theories are discussed. For N ? 4 we find self duality in four dimensions and we give the transition points. For N > 4 these systems are not self dual. Also, the order parameter is discussed. The general Z(N) gauge theory is found to be self dual for all N.     

Large N expansion for Yukawa-type theories

4 dimensional Yukawa-type theories with an internal SU(N) symmetry group are studied in the large N limit by means of path integral techniques. For a simplified model where the bosonic field transforms as a singket under SU(N), we explicitly solve the gap equation and shiw that the symmetry is spontaneously broken.     

SU(N) invariant non-linear σ models

Two series of SU(N) invariant non-linear σ models are constructed using exceptional orbits of the adjoint representation of SU(N). Each of these models possesses infinitely many local as well as non-local conserved charges.     

Kinematics of periodic structures in SU(N) gauge theories

We study periodicity by use of the holonomy group. For a general field configuration, which spans the whole SU(N) group, we show that periodicity of gauge-invariant quantities implies that either the flux is quantized or that there is no flux at all. Finally we show that in a special gauge, the quantized 't Hooft flux can be expressed as a line integral over one of the components of the vector potential. The other components then have “Higgs-like” zeros, with winding numbers related to the 't Hooft flux.     

SU(N) group-theory constraints on color-ordered five-point amplitudes at all loop orders

Color-ordered amplitudes for the scattering of n particles in the adjoint representation of SU(N) gauge theory satisfy constraints arising solely from group theory. We derive these constraints for n=5 at all loop orders using an iterative approach. These constraints generalize well-known tree-level and one-loop group theory relations.     

Spectrum of lattice gauge theories with fermions from a 1/d expansion at strong coupling

We study the strong coupling limit of U(N) or SU(N) gauge theories with fermions on a lattice. The integration over the gauge and fermion degrees of freedom is performed by analytic methods, leading to a partition function in terms of localized meson and baryon fields. A method for deriving a systematic expansion in the inverse of the space-time dimension of the corresponding Green functions is developed. It is applied to the study of spontaneous breakdown of chiral symmetry, which occurs for any U(N) or SU(N) theory with fermions in the fundamental representation. Meson and baryon spectra are then computed, and found to be in close agreement with those obtained by numerical methods at finite coupling. The pion decay constant is estimated.     

Non-local continuity equations for self-dual SU(N) Yang-Mills fields

Using a manifestly gauge invariant formulation, an infinite set of classical non-local continuity equations is constructed for the self-dual SU(N) Yang-Mills fields.     

Grand unified theories in the framework of the SU(N) group

Due to the problem of flavour, the general SU(N) gauge group is considered as a candidate for grand unification. Starting from a set of general requirements, we find restrictions and conditions for the construction of grand unified theories within the framework of such a group. The allowed groups get restricted to SU(6), SU(7) and SU(8).     

Inequalities for order and disorder parameters in SU(N) gauge theories

We discuss inequalities of the Mack-Fröhlich type in SU(N) gauge theories and their possible implications for the various phases of those theories.