International Journal of Modern Physics A

We review various ways of obtaining consistency between the idea of supersymmetric grand unification and an apparent low value of α_s~0.112 indicated by several low energy experiments. We argue that to reconcile the low value of α_s with the predictions of supersymmetric GUT’s, we need to go beyond the standard minimal supersymmetric GUT scenario and invoke new physics either at 10¹¹–10¹² GeV or at the GUT scale.

In the first part, the induced vacuum spin around an Aharonov-Bohm flux string in massless three-dimensional QED is computed explicitly and the result is shown to agree with a general index theorem. A previous observation in the literature, that the presence of induced vacuum quantum numbers which are not periodic in the flux make an integral-flux AB string visible, is reinforced. In the second part, a recent discussion of chiral symmetry breaking by external magnetic fields in parity-invariant QED₃ and its relation to the induced spin in parity-noninvariant QED₃ is further elaborated. Finally, other vacuum polarization effects around flux tubes in different variants of QED, in three and four dimensions are mentioned.

We show that the large N partition functions and Wilson loop observables of two-dimensional Yang-Mills theories admit a universal functional form irrespective of the gauge group. We demonstrate that U(N) QCD₂ undergoes a large N, third order phase transition on the projective plane at an area coupling product of π²/2. We use this as a lemma to provide a direct transcription for the partition functions and phase portraits of Yang-Mills theory from the U(N) on RP² at large N to the other classical Lie groups on S². We compute the expectation value of the Wilson loops in the fundamental representation for SO(N) and Sp(N) on the two-sphere. Finally we compare the strong and weak coupling limit of these expressions with those found elsewhere in the literature.

Using the representation of the quantum group SL_q(2) by the Weyl operators of the canonical commutation relations in quantum mechanics, we construct and solve a new vertex model on a square lattice. Random variables on horizontal bonds are Ising variables, and those on the vertical bonds take half positive integer values. The vertex is subjected to a generalized form of the so-called “ice rule,” its property is studied in detail and its free energy calculated with the method of quantum inverse scattering. Remarkably, in analogy with the usual six-vertex model, there exists a “free-fermion” limit with a novel rich operator structure. The existing algebraic structure suggests a possible connection with a lattice neutral plasma of charges, via the fermion-boson correspondence.

The general theory of N=1 supergravity with supermatter is applied to a Bianchi type IX diagonal model. The supermatter is constituted by a complex scalar field and its fermionic partners. The Kähler geometry is chosen to be a two-dimensional flat one. The Lorentz-invariant ansatz for the wave function of the universe is taken to be as simple as possible in order to obtain new solutions. The set of differential equations derived from the quantum constraints are analyzed in two different cases: if the supermatter terms include an analytical potential or not. In the latter the wave function is found to have a simple form.

In this article, we analyze multimatrix chain models. They can be considered as multicomponent Toda lattice hierarchies subject to suitable coupling conditions. The extension of such models to include extra discrete states requires a weak form of integrability. The discrete states of the q-matrix model are organized in representations of sl_q. We solve exactly the Gaussian type models, of which we compute several all-genus correlators. Among the latter models one can classify also the discretized c=1 string theory, which we revisit using Toda lattice hierarchy methods. Finally, we analyze the topological field theory content of the 2q-matrix models: we define primary fields (which are ∞^q), metrics and structure constants, and prove that they satisfy the axioms of topological field theories. We outline a possible method for extracting interesting topological field theories with a finite number of primaries.

We investigate the question of how the knowledge of sufficiently many local conservation laws for a model can be used to solve it. We show that for models where the conservation laws can be written in one-sided forms, like the problem can always be reduced to solving a closed system of ordinary differential equations. We investigate the A₁, A₂ and B₂ Toda field theories in considerable detail from this viewpoint. One of our findings is that there is in each case a transformation group intrinsic to the model. This group is built on a specific real form of the Lie algebra used to label the Toda field theory. It is the group of field transformations which leaves the conserved densities invariant.

Continuing our recent argument where we constructed a FNBWW type spin-1 boson having opposite relative intrinsic parity to that of the associated antiparticle, we now study eigenstates of the charge conjugation operator. Based on the observation that if ϕ_L(p^μ) transforms as a (0, j) spinor under Lorentz boosts, then transforms as a (j, 0) spinor [with a similar relationship existing between ϕ_R(p^μ) and where w ith Θ[j] the well-known Wigner matrix involved in the operation of time reversal] we introduce McLennan-Case type (j, 0)⊗(0, j) spinors. Relative phases between ϕ_R(p^μ) and and and ϕ_L(p^μ), turn out to have physical significance and are fixed by appropriate requirements. An explicit construction, and a series of physically relevant properties, for these spinors are obtained for spin-1/2 and spin-1 culminating in the construction of a new wave equation and the introduction of Dirac-like and Majorana-like quantum fields.