Late Time Isotropy Viewed Through Bianchi Type I Cosmological Models with Vacuum Energy

We investigate Bianchi type I cosmological models for perfect fluid source with time-dependent cosmological term Λ. We explore the possibility of cosmological models assuming the expansion anisotropy (the ratio σ/θ of the shear scalar σ to the volume expansion θ) to be a function of average scale factor R. The resulting models begin with initial anisotropy and approach isotropy at late times. The models evolve with decelerating expansion and enters into accelerating phase for large values of t.     

σ models in even-dimensional spaces

We propose a class of grassmannian models in 2k dimensions which for k = 1 reduce to CP^N?1 models and for k = 2 to composite SU(2) Yang-Mills models. We define and discuss the conditions of self-duality for these models and present corresponding one-instanton field configurations. Some properties of these configurations are briefly discussed.     

Vertex models on Feynman diagrams

We discuss the statistical mechanics of vertex models on both generic (“thin”) and planar (“fat”) random graphs. Such models can be formulated as the N → 1 and N → ∞ limits of N × N complex matrix models, respectively. From the graph theoretic perspective one is using matrix model and field theory inspired methods to count various classes of directed graphs. For the thin random graphs we use saddle point methods to solve the models in the thermodynamic, large number of vertices limit and note that, as in the case of the eight-vertex model on the square lattice, various other models such as the Ising model appear as particular limits. The generic solution of the fat graph model is rather more elusive, but we show that for several choices of the couplings the models can be reduced to eigenvalue integrals and their critical behaviour deduced.     

The weak-coupling phase of lattice spin and gauge models

We analyze the lattice weak-coupling (w.c.) expansion of O(N), CP^N?1 and chiral spin models, and of large-N reduced chiral and gauge models.We find that the w.c. expansion always agrees with mean field results, whenever comparable, for arbitrary space-time dimensions, and that the expansion of the reduced models agrees with that of the original ones. However, w.c. results disagree with one-dimensional large-N and (old and new) exact results. We explain this phenomenon as a failure of the analytic continuation from higher dimensions that defines lattice w.c. perturbation theory for massless models (even if infrared singularities always cancel).We use an improved version of the mean field (m.f.) technique suitable for reduced models. We compute the m.f. approximation of chiral models and use this result to determine the large-d (m.f.) behaviour of reduced gauge models, finding agreement with standard Wilson theory results.We give a new characterization of large-N chiral models in terms of the single-link integral for the adjoint representation of SU(N).     

Massive lepton pair production as a test of models for particle production on nuclei

The nuclear-size dependence of massive lepton pair production on nuclei is found to provide a selective test of models describing hadron-nucleus interactions. In particular, a clear discrimination is possible between two types of models: the sequential multiple scattering models with energy degradation, and the “parallel” multiple scattering models with a long time scale involved. Both types of models are known to describe equally well the distributions of hadrons produced on nuclei. It is shown, however, that the observedA ¹-dependence of theD-Y process rules out the sequential scattering models as well as some oversimplified versions of the parallel multiple scattering models.     

Integrable aspects of the scaling q-state Potts models II: finite-size effects

We continue our discussion of the q-state Potts models for q⩽4, in the scaling regimes close to their critical and tricritical points. In a previous paper, the spectrum and full S-matrix of the models on an infinite line were elucidated; here, we consider finite-size behaviour. TBA equations are proposed for all cases related to φ₂₁ and φ₁₂ perturbations of unitary minimal models. These are subjected to a variety of checks in the ultraviolet and infrared limits, and compared with results from a recently-proposed non-linear integral equation. A non-linear integral equation is also used to study the flows from tricritical to critical models, over the full range of q. Our results should also be of relevance to the study of the off-critical dilute A models in regimes 1 and 2.     

Spontaneous supersymmetry breaking by large-N matrices

Motivated by supersymmetry breaking in matrix model formulations of superstrings, we present some concrete models, in which the supersymmetry is preserved for any finite N, but gets broken at infinite N, where N is the rank of matrix variables. The models are defined as supersymmetric field theories coupled to some matrix models, and in the induced action obtained after integrating out the matrices, supersymmetry is spontaneously broken only when N is infinity. In our models, the large value of N gives a natural explanation for the origin of small parameters appearing in the field theories which trigger the supersymmetry breaking.     

Membrabe models and generalized Z2 gauge theories

We consider models of (d?n)-dimensional membranes fluctuating in a d-dimensional space under the action of surface tension. We investigate the renormalization properties of these models perturbatively and in $\text{1}\text{n}$ expansion. The potential relationships of these models to generalized Z₂ gauge theories are indicated.     

Construction of nonlinear σ-models in two and higher space-dimensions

An algorithm for constructing nonlinear σ-models in arbitrary space-dimensions m (m ≥ 2) is proposed and Hamiltonian estimates are found through the degree of mapping. The field models are constructed in general forms and the scaling-neutral models are shown to have exact soliton solutions which are (anti) self-dual when the corresponding topological charge is the degree of mapping. All known field models are shown to be particular cases of the general models proposed, which also give new models not investigated before.     

Two dimensional gases of weight charges and SU(N) fermino theories

We analyze two dimensional gases composed of particles interacting via a Coulomb or Yakawa potential through their “non-Abelian” charges. These charges are taken to be elementary weight or root vectors of SU(N). The grand partition function of these gases is shown to be equivalent to the generating functional of sine-Gordon models with weight vectors and hence to that of SU(N) fermion models. The fermion field creates or annihilates topological solitons which have elementary weight vectors as topological quantum numbers. Then, we discuss the confinement of fermions in the SU(N) Higgs models, where instantons (Z_N vortices) constitute a Yukawa gas of weight charges. We prove that fermions are confirmed by the effects of instantons in the SU(N) Higgs models in contrast with the Abelian Higgs model.     

Muon-electron transitions in models of radiative lepton masses

In models where both the electron and muon acquire radiative masses, the same mechanism often allows μ-e transitions as well at a certain level. We discuss the phenomenological constraints on some recently proposed models of this type and show that they are incompatible with present experimental limits on μ→eγ, and in one case also μ→eee, without the fine tuning of parameters which these models are supposed to avoid.     

The CPN−1 model: A strong coupling lattice approach

We develop large N character-like expansion techniques for vector and vector-like models. These are used to compute the mass gaps and beta functions in the d = 2 CP^N?1 models. Surprisingly there is an intermediate region where neither strong coupling nor perturbation theory is applicable. This “unknown” region is a consequence of the non-commutativity of strong coupling and large N, an interesting mathematical effect not found in other models and due to an interesting physical phenomenon: superconfinement.     

A study of the critical behavior of the O(N) linear and nonlinear σ models

A study of the large N behavior of both the O(N) linear and nonlinear σ models is presented. The purpose is to investigate the relationship between the disordered (ordered) phase of the linear and nonlinear sigma models. Utilizing operator product expansions and stability analyses, it is shown that for 2 ≤ d < 4, it is the dimensionless renormalized quartic coupling and $\text{λ}{}^1$ is the IR fixed point) limit of the linear σ model which yields the nonlinear σ model. It is also shown that stable large N linear σ models with λ < 0 (σ is the bare quartic coupling) can exist (at least in the context of no tachyonic states being present). A criteria valid for all dimensionalities d, less than four, is derived which determines when λ < 0 models are tachyonic free. Arguments are given showing that the d = 4 large N linear (for λ > 0) and nonlinear models are trivial. This result (i.e., triviality) is well known but only for one and two component models. Interestingly enough, the λ < 0, d = 4 linear σ model remains nontrivial and tachyonic free.     

The Six and Eight-Vertex Models Revisited

Elliott Lieb's ice-type models opened up the whole field of solvable models in statistical mechanics. Here we discuss the “commuting transfer matrix” T,Qequations for these models, writing them in a more explicit and transparent notation that we believe offers new insights. The approach manifests the relationship between the six-vertex and chiral Potts models, and between the eight-vertex and Kashiwara–Miwa models.     

Hodge theory used to produce finite self-energy models of the electron

The relationship between electromagnetic fields and topology is discussed. Hodge theory is generalized to classify static fields in static wormhole models. This generalization is used to show models of the electron exist which have finite self-energy. These models always have 1/R ² electric fields and self-energies of 4πq ²/R ₀, whereR ₀ is the inner radius of the wormhole.     

A generalization of the Virasoro algebra to arbitrary dimensions

Colored tensor models generalize matrix models in higher dimensions. They admit a 1/N expansion dominated by spherical topologies and exhibit a critical behavior strongly reminiscent of matrix models. In this paper we generalize the colored tensor models to colored models with generic interaction, derive the Schwinger Dyson equations in the large N limit and analyze the associated algebra of constraints satisfied at leading order by the partition function. We show that the constraints form a Lie algebra (indexed by trees) yielding a generalization of the Virasoro algebra in arbitrary dimensions.     

On the bifurcations occuring in the parameter space of the sixteen vertex model: I. Discrete bifurcations

The 16-dimensional parameter space of homogeneous sixteen vertex models is scanned for bifurcation points, i.e. points corresponding to models which possess extra symmetries not existing in nearby points. Equivalence classes of models having the same partition function are identified by means of a characteristic “normal” model, represented by a (4 x 4)-diagonal matrix N, and a pair of (2 x 2)-matrices A and B. In this paper the matrix N is assumed to be non-degenerate and the only bifurcations found are those associated with special types of matrices A and B, i.e. matrices whose decomposition in terms of Pauli-matrices corresponds to a vector a ≡ (a₁, a₂, a₃) or b ≡ (b₁, b₂, b₃) that is invariant with respect to one or more elements of the cubic symmetry group.The various bifurcation classes of models found include: a) the families of general- and “complementary” eight vertex models, b) discrete sets of doubly- and one-sided cyclic models and c) a number of secondary bifurcation classes within the eight-vertex families, among which is Baxters symmetric eight-vertex model.     

A class of “natural” composite models

The starting point is the attractive class of composite models where quarks and leptons appear as fermion-scalar bound states (Fφ). The aim is to resolve the “naturality” problem associated with fundamental scalars without losing the appealing properties of Fφ-type composite models. A systematic construction of such models is given, where the scalar constituents automatically qualify as light dynamical scalars, i.e. as composite (pseudo) Goldstonebosons. A comfortably large class of composite models then results, where all standard “naturality” requirements are satisfied: the quark and lepton masses are kept small through 't Hooft's chiral protection mechanism; the dynamical scalar “constituents” are light and the CP problem of QCD finds an automatic solution. Further characteristics are economy, absence of light exotics, possibility of three generations and elegance of anomaly matching. It is shown that existing attractive models with fundamental scalars can be made “natural” in the sense defined above.