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.     

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.     

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.     

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.     

Gaussian fluctuations to U(N) and SU(N) lattice gauge theories in the mean field approximation

The mean field can be considered as a classical solution of an appropriately reformulated version of lattice gauge theories. Axial gauge fixing renders it stable. The quadratic forms for the fluctuations in the gaussian approximation are analyzed. The gaussian correction to the mean field free energy is expressed for all U(N) and SU(N) in terms of structure functions that are explicitly calculated for U(N), SU(∞, and SU(∞) numerical calculations are performed for the phase transition point, its latent heat, and some correlation lengths that are characteristic for this kind of mean field approach.     

Effective SU(2) × SU(2) symmetry violations generated by electromagnetic and weak interactions

The interplay among the SU(3) × SU(3) violating interaction and the electromagnetic and weak interactions is considered in the context of the (3,3^∗)+(3^∗,3) symmetry breaking model. It is argued that the symmetry breaking Hamiltonian determined phenomenologically represents the effective interaction which generates the tadpole contributions coming from all symmetry violating interactions.     

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.     

A universal covering group of SU(p, q)

A universal covering group of SU(p, q) is parametrized and its groups law in this parametrization is established.     

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.     

On the connection of matrix elements of the SU (1,1) discrete series representations with SU (2) matrix elements

The purpose of this note is to establish the connection between the matrix elements of representations of two simplest groups: representations of the discrete series of the non-compact SU (1,1) group and the corresponding representations of the compact SU (2) group.     

Unified field theories with U(N) internal symmetries: G

Gauge theories for extended SU(N) conformal supergravity are constructed which are invariant under local scale, chiral, proper conformal, supersymmetry and internal SU(N) transformations. The relation between intrinsic parity and symmetry properties of their generators of the internal vector mesons is established. These theories contain no cosmological constants, but technical problems inherent to higher derivative actions are pointed out.     

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.     

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).     

Bound states in N = 8 supergravity and N = 4 supersymmetric Yang-Mills theories

We present a study of possible bound states in N = 8 supergravity. We find evidence for the existence of multiplets of two-body bound states and expect that many-body bound states may exist as well. Our study is based on a calculation of Regge trajectories in the two-body scattering amplitudes of the lagrangian field theory. We also study Regge trajectories in N = 4 Yang-Mills theory and find evidence for a possible spin zero, SU(4) and gauge singlet, massless bound state. If such a state actually exists and supersymmetry is not broken, it may be a member of a supersymmetric multiplet which includes the graviton.     

Off-shell N = 8 supersymmetry with central charges

Using a new technique of dimensional reduction by Legendre transformation we derive an off-shell formulation of the N = 8 extended supersymmetry algebra, which is realised in the maximally extended supergravity theory. The theory has an Sp(8) manifest global invariance and some of the fields satisfy differential constraints.     

Factorizable Z(N) models

The factorizable S-matrix with Z(N) symmetry is constructed. It is speculated that the field theory belonging to this S-matrix matrix is related to the scaling limit of Z(N) generalizations of the Ising model.     

Equivalent lagrangians in large N field theories

The auxiliary field method is generalized to any O (N)-invariant theory with non-polynomial interactions. In non-supersymmetric theories, two lagrangians with and without an auxiliary field are shown to be equivalent to the leading order of the 1/N expansion. In supersymmetric theories, these two lagrangians are equivalent to all orders of the 1/N expansion. The lagrangian with an auxiliary field is solvable in the 1/N expansion.     

Representations of the Sugawara SU(2) current algebra

The Sugawara SU(2) current algebra is exponentiated in order to obtain the group. Further, the representations of the current algebra are recovered from the representations of the group.Generators of the three-dimensional Euclidean group E, (space translations and space relations) are constructed. An example showing the relation with Yang-Mills theory is presented.     

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.