Spin and isospin in a gauge theory with monopoles

The mechanism by which systems of spinless bosons with isospin and spinless magnetic monopoles acquire a spin in their ground states is investigated in the context of SU(2) gauge models. Contrary to recent claims, it is demonstrated that isospin degrees of freedom are not converted into spin degrees of freedom. For a spin $\text{1}\text{2}$ state, solutions are explicitly constructed, exhibiting the isospin degree of freedom.     

Flavour and superunification

We consider the possibility of a non-trivial embedding of $\text{(}\text{10}\text{+}\text{5}\text{)}\text{SU}\text{(5)}$ families of spin if$\text{1}\text{2}$ left-handed fermions in a combination of irreducible massless supermultiplets of N extended supersymmetry. We demand the whole spectrum of spin $\text{1}\text{2}$ states to be anomaly free with respect to SU(N). This turns out to be a necessary condition for the absence of anomalies at the SU(5) level. We find two classes of models, with spin $\text{1}\text{2}$ fermions in SU(N) representations associated to one- and two-column Young tableaux, respectively, in which each irreducible massless multiplet occurs at most once. These two classes of models lead to a nontrivial family generation due to supersymmetry. For N = 8 extended supersymmetry, they give at most three and five families, respectively. The first class of models is more natural in the way it excludes SU(5) exotics. The same analysis is extended to the massless multiplets that can be obtained from bilinear composite fields of the (preonic) elementary fields of N extended supergravity. We prove that the generation of families requires the repetition of massless multiplets and that ($\text{10 +}\text{5}$) SU(5) families can only be generated in pairs. General properties of multilinear composite operators of the preonic fields are given and the rôle of massive representations to classify towers of operators with definite spin is pointed out.     

Gauged N = 8 supergravity in five dimensions

We construct gauged N = 8 supergravity theories in five dimensions. Instead of the twenty-seven vector fields of the ungauged theory, the gauged theories contain fifteen vector fields and twelve second-rank antisymmetric tensor fields satisfying self-dual field equations. The fifteen vector fields can be used to gauge any of the fifteen-dimensional semisimple subgroups of SL(6,R), specially SO(p, 6?p) for p = 0, 1, 2, 3. The gauged theories also have a physical global SU(1,1) symmetry which survives from the E₆₍₆₎ symmetry of the ungauged theory. This SU(1,1) for the SO(6) gauging is presumably related to that of the chiral N = 2 theory in ten dimensions. In our formalism we maintain a composite local USp(8) symmetry analogous to SU(8) in four dimensions.     

A local mixed valence model

We consider a purely electronic model for local valence fluctuations consisting of a spinless localized 4f-level interacting with spinless extended 5d-states. We show that (a) the impurity model is related to the anisotropic Kondo problem, (b) a single 4f-level behaves like a resonant level with temperature-dependent width and (c) these results, when extended to a concentrated system of local incoherent mixed valence levels, are qualitatively in agreement with the main experimental features for mixed valence compounds.     

Baryons in the effective lagrangian of strongly coupled lattice QCD

The effective action formulation of lattice QCD is extended to incorporate baryons. At strong coupling we find a generalized σ model where the baryons obtain their mass via a non-vanishing vacuum expectation value 〈¯ΦΦ〉. The SU(3) effective potential is worked out for Susskind fermions taking into account the influence of the baryons, and the results are compared with the U(3) theory. The large-N behavior of the SU(N) theory is studied as well. A loop expansion method is proposed for dealing with general multi-component baryon fields in both Susskind's and Wilson's fermion formulations.     

Negative dimensions and E7 symmetry

The invariant length and volume which characterize the Lorentz group are extended to a quadratic and a quartic supersymmetric invariant. The symmetry group of the Grassmann sector can be SO(2), SU(2), SU(2) × SU(2) × SU(2), Sp(6), SU(6), SO(12) or E₇, which are also possible global symmetries of extended supergravities. Diophantine conditions which yield this classification follow from the corresponding conditions in d bosonic dimensions by the replacement d → ?d.     

Phases of resonant amplitudes: πN → πΔ

The phases of resonant amplitudes in πN → πΔ are studied in a modified version of SU(6)_W in which amplitudes involving different relative orbital angular momenta l are uncoupled form one another. This form of SU(6)_W is equivalent to one studied recently by Melosh, in which the set of selection rules for decays is extended to allow for more types of transition than in the original version of this symmetry.The predictions are compared with a recent preliminary analysis by Herndon et al. Even the extended (“l-broken”) version of SU(6)_W is found to disagree with the present experimental solution. If this solution persists, it constitutes the strongest present evidence against such a symmetry.     

Bare current-quark masses,inelastic reactions and light-cone algebra

Relations connecting the effective bare current-quark masses with asymptotic meson-nucleon and lepton-nucleon scattering are derived by making use of the extended light-cone algebra which includes commutators of pseudoscalar densities. The commutators are relevant to meson-nucleon scattering amplitudes since the pseudoscalar densities act as fields of the (composite) mesons. Assuming pomeron-exchanged Regge behaviour, sufficient analyticity in the meson mass-squared variable is established to obtain finite-mass dispersion and superconvergence relations. Making additionally certain other reasonable assumptions, we are then able to show how these relations yield testable connections among the asymptotic πN and KN total cross sections, the structure functions of the deep inelastic lepton-nucleon scattering (for the scaling variable, ξ →0) and the bare current-quark masses μ_{p, n, λ} that appear essentially as parametrising the breaking of the chiral SU(3) ? SU(3) symmetry. One interesting consequence of our results is at the Llewellyn-Smith inequality on the said structure functions should be experimentally satisfied as a near equality for ξ → 0, if chiral SU(2) ? SU(2) turns out to be a rather good symmetry of nature. Moreover, taking the specific symmetry breaking model of Gell-Mann Oakes and Renner,we find that μ_{p, n} ≈ 35 MeV and μ_λ ≈ 800 MeV.     

Possibility of a doubly-charged structure at theS-meson mass

The various symmetry breaking patterns that are possible with a 24-plet and a 5-plet of Higgs fields in SU(5) are classified. Spontaneous breakdown of SU(5) to SU(3)_colour×U(1) _em can be achieved (excluding the gauge hierarchy problem) without imposing unnatural constraints on the parameters of the Higgs potential.     

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.     

Curiosities at c = 1

We consider conformal field theories on a torus with central charge c = 1, and in particular models based upon modding out string propagation on the SU(2) group manifold by its finite subgroups. We find that the partition functions for these models coincide with the continuum limit partition functions of a recently introduced class of RSOS models, defined in terms of the extended Dynkin diagrams of simply-laced Lie algebras, thus giving an alternative interpretation for the primary fields in these latter theories. Three of the models have no massless moduli and thus do not lie on the same line of critical points with the rest. The particular correspondence between simply-laced Lie algebras and finite subgroups of SU(2) that emerges coincides with that which has already appeared in other mathematical contexts.     

Mass scale of grand unification in N = 8 extended supergravity

The mass scale for the running coupling of the conjectured SU(5) grand unified theory embedded in N = 8 extended supergravity is shown to (almost) coincide with the Planck mass. Furthermore, the masses of the superheavy particles in the theory are expected to be order O(m_X) rather than O(m_Planck).     

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.     

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.     

On the structure of the QCD vacuum in the large-N limit

We present an approximate QCD vacuum for SU(N → ∞). It is a generalization of the ferromagnetic vacuum first obtained by Savvidy for SU(2) and generalized by one of us to SU(3) and SU(4). Problems occuring for N ? 5 are handled in the large-Nlimit by a contnious formalism, and the vacuum obtained is characterized by N ? 1 constant, commuting, color magnetic fields with an isotropic distribution of spatial directions. The energy density of this vacuum is lower than of the perturbative vacuum by a number proportional to N², as expected from general large-N arguments. Like the Savvidy vacuum the large-N vacuum may decay into a variant of the domained Copenhagen vacuum. We give a lower limit on the domain size.     

On-shell and conformal N = 4 supergravity in superspace

We discuss the superspace geometries which are necessary to describe on-shell O(4) and SU(4) supergravity. The relation of central charge field strengths to physical spin-zero fields is exhibited and a “new” O(4) theory is shown to exist. The version of SU(4) supergravity which uses an antisymmetric tensor gauge field is found to require modifications of ordinary superspace. Finally the Poincaré supergeometry which admits the conformal N = 4 supermultiplet is constructed. It is shown that consistency of the Bianchi identities implies the existence of dimension zero auxiliary fields which are components of a non-linear multiplet.     

Formulation of 11-dimensional supergravity in superspace

We formulate on-shell 11-dimensional supergravity in superspace and express its equations of motion in terms of purely geometrical quantities. All torsion and curvature components are solved in terms of a single superfield W_rstu, totally antisymmetric in its (flat vector) indices. The dimensional reduction of this formulation is expected to be related to the superspace formulation of N=8 extended supergravity and might explain the origin of the hidden (local) SU(8) and (global) E₇ symmetries present in this theory.     

Constraints on the currents in principal models giving rise to integrable nonlinear systems

Quadratic constraints on the current in the principal SU(2n) model stand at the origin of an extended reduction mechanism. We derive local conservation laws both for the reduced model and for a class of solutions of the principal SU(2n) model.     

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).     

Extended hubbard model with ring exchange: a route to a non-Abelian topological phase

We propose an extended Hubbard model on a 2D kagome lattice with an additional ring exchange term. The particles can be either bosons or spinless fermions. We analyze the model at the special filling fraction 1/6, where it is closely related to the quantum dimer model. We show how to arrive at an exactly soluble point whose ground state is the "d-isotopy" transition point into a stable phase with a certain type of non-Abelian topological order. Near the "special" values, d=2cos(pi/(k+2), this topological phase has anyonic excitations closely related to SU(2) Chern-Simons theory at level k.