Multi-Trace Superpotentials vs. Matrix Models

We consider ᵊ9=1 supersymmetric U(N) field theories in four dimensions with adjoint chiral matter and a multi-trace tree-level superpotential. We show that the computation of the effective action as a function of the glueball superfield localizes to computing matrix integrals. Unlike the single-trace case, holomorphy and symmetries do not forbid non-planar contributions. Nevertheless, only a special subset of the planar diagrams contributes to the exact result. In addition, the computation of the superpotential localizes to doing matrix integrals. In view of the results of Dijkgraaf and Vafa for single-trace theories, one might have naively expected that these matrix integrals are related to the free energy of a multi-trace matrix model. We explain why this naive identification does not work. Rather, an auxiliary single-trace matrix model with additional singlet fields can be used to exactly compute the field theory superpotential. Along the way we also describe a general technique for computing the large-N limits of multi-trace Matrix models and raise the challenge of finding the field theories whose effective actions they may compute. Since our models can be treated as ᵊ9=1 deformations of pure ᵊ9=2 gauge theory, we show that the effective superpotential that we compute also follows from the ᵊ9=2 Seiberg-Witten solution. Finally, we observe an interesting connection between multi-trace local theories and non-local field theory.     

<Emphasis Type="Italic">N</Emphasis>=4 SYM and QCD motivated approach to soft interactions at high energies

In this paper we construct a model that satisfies the theoretical requisites of high energy soft interactions, based on two ingredients: (i) the results of N=4 SYM, which at present is a unique theory that allows one to deal with a large coupling constant; and (ii) the requirement of matching with high energy QCD. In accordance with these ideas, we assume that the soft Pomeron intercept is relatively large, and the slope of the Pomeron trajectory is equal to zero. We derive analytical formulae that sum both enhanced and semi-enhanced diagrams for elastic and diffractive amplitudes. We fit the available experimental data, and predict the value for cross sections at the energies accessible at the LHC and beyond. The main corrections to the model are studied and evaluated.     

On accuracy of different cluster models used in describing ordering phase transitions in fcc alloys

A general formulation of cluster methods applied to calculations of thermodynamic quantities of alloys in terms of renormalizing fields describing interaction between a cluster and its environment is given. We have shown that the well-known cluster variation method and the cluster field method, which was suggested earlier, are special cases of our approach. These methods have been used in calculations of phase diagrams of fcc alloys with L1₂ and L1₀ ordering transitions with several realistic interaction models. It turns out that, for all these models, the simple tetrahedron version of the cluster field method suggested in this paper describes the phase diagrams almost as accurately as more complicated cluster variation techniques. Possible applications of the tetrahedron version of the cluster field method to inhomogeneous states and kinetics of phase transitions in fcc alloys are discussed. Zh. éksp. Teor. Fiz. 115, 158–179 (January 1999)     

Being Discrete about Yang and Mills: Basic Techniques of Euclidean Lattice Gauge Theory

We discuss the formulation of gauge-invariant quantum field theories (without dynamical matter fields) as statistical mechanics systems on four-dimensional Euclidean lattices. Approximation methods including strong- and weak-coupling expansions, mean-field theory and Monte Carlo simulations are reviewed in detail, and Abelian duality transformations are derived. New models are discussed. An action is defined on 2 × 1 rectangular loops of links and its properties are investigated. It is found to result in phase transitions in 2, 3 and 4 dimensions with Z(2) and SU(2) gauge groups. A large class of models with Z(N) symmetry realised on plaquettes is investigated, and several phase diagrams are presented. A mixed model with interactions through both plaquettes and rectangles is found to have a line of phase transitions and a critical point associated with the crossover region in the Wilson SU(2) model.     

Constraints on unified models for dark matter and dark energy using <Emphasis Type="Italic">H</Emphasis>(<Emphasis Type="Italic">z</Emphasis>)

The differential age data of astrophysical objects that have evolved passively during the history of the universe (e.g. red galaxies) allows us to test theoretical cosmological models through the predicted Hubble function expressed in terms of the redshift z, H(z). We use the observational data for H(z) to test unified scenarios for dark matter and dark energy. Specifically, we focus our analysis on the Generalized Chaplygin Gas (GCG) and the viscous fluid (VF) models. For the GCG model, it is shown that the unified scenario for dark energy and dark matter requires some priors. For the VF model we obtain estimations for the free parameters, which may be compared with further analysis mainly at perturbative level.     

Path integrals in polar field variables in QFT

We show how to transform a d-dimensional Euclidean path integral in terms of two (Cartesian) fields to a path integral in terms of polar field variables. First we present a conjecture that states how this transformation should be done. Then we show that this conjecture is correct in the case of two toy models. Finally the conjecture will be proven for a general QFT model with two fields.     

Interacting fermions on a random lattice

We extend previous work on the properties of the Dirac lagrangian on two-dimensional random lattices to the case where interaction terms are included. Although for free fermions the chiral symmetry of the doubles is spontaneously broken by their interaction with the lattice and they decouple from long-distance physics, our results in this paper show that all is undone by quantum corrections in an interacting field theory and that the end result is very similar to what is found with Wilson fermions. Two field-theoretical models with interacting fermions are studied by perturbation expansion in the field theory coupling constant. These are a model with one fermion and one boson species interacting via a scalar Yukawa coupling and the massive Thirring model. It is shown that on the random lattice ultraviolet finite diagrams and finite parts of ultraviolet divergent diagrams have the correct continuum limit. Ultraviolet divergent parts can be removed by the same renormalisation procedure as in the continuum, but do not exhibit the same dependence on the lagrangian mass. In the case of the massive Thirring model this causes a fermion mass correction of order the cut-off scale, which breaks the chiral symmetry of the remaining light fermion; there is consequently a fine-tuning problem. In the context of the same model we discuss the effect of the Goldstone boson associated with the spontaneous breakdown of the chiral symmetry of the doubles on two-dimensional models with vector couplings.     

Tachyon field in cosmology

We study cosmological effects of homogeneous tachyon field as dark energy. We concentrate on two different scalar field potentials, the inverse square potential and the exponential potential. These models have a unique feature that the matter density parameter and the density parameter for tachyons remain comparable for a large range in red-shift. It is shown that there exists a range of parameters for which the universe undergoes an accelerated expansion and the evolution is consistent with structure formation requirements. For a viable model we require fine tuning of parameters comparable to that in ACDM or in quintessence models. For the exponential potential, the accelerated phase is followed by a phase witha(t) α t ^2/3 thus eliminating a future horizon.     

Network models: Action formulation

We develop a technique to formulate quantum field theory on an arbitrary network, based on different randomly disposed sets of scattering points. We define the R-matrix of the whole network as a product of R-matrices attached to each scattering node. Then an action is formulated for a network in terms of fermionic fields, which allows to calculate the transition amplitudes as Green functions. On so-called bubble and triangle diagrams it is shown that the method produces the same results as the one which uses the generalized star product. The approach allows to extend network models by including multiparticle interactions at the scattering nodes.     

Dimensionality Effects on the Mixed Spin-1/2 and Spin-2 Blume-Capel Model: Renormalization Group Theory

We have used the real-space Migdal-Kadanoff renormalization group technique on d-dimensional hypercubic lattice to study the mixed spin-1/2 and spin-2 Blume-Capel model. First, we indicate a critical dimension d_C ≈?2.05, above and below which different topologies of phase diagrams occur. The phase diagrams have been plotted in the (crystal field, temperature) plane around d_C, in which there is a second-order phase transition. Moreover, using the variation of the free energy at low temperatures, we have established the ground-state phase diagrams in the (?/J, C/J) plane for d?<?d_C and d?≥?d_C. In particular, we have seen the appearance of two first-order transitions at very low temperatures by the use of the free energy and its isotherm derivative. A detailed analysis of fixed points and flow diagrams indicates that there is no tricritical point.

     

Functional Closure of Schwinger-Dyson Equations in Quantum Electrodynamics: 1. Generation of Connected and One-Particle Irreducible Feynman Diagrams

Using functional derivatives with respect to free propagators and interactions we derive a closed set of Schwinger-Dyson equations in quantum electrodynamics. Its conversion to graphical recursion relations allows us to systematically generate all connected and one-particle irreducible Feynman diagrams for the n-point functions and the vacuum energy together with their correct weights.     

Gauge coupling and fermion mass relations in low string scale brane models

We analyze the gauge coupling evolution in brane inspired models with U(3) x U(2) x U(1)^N symmetry at the string scale. We restrict our work to the case of brane configurations with two and three abelian factors (N = 2,3) and where only one Higgs doublet is coupled to down quarks and leptons and only one to the up quarks. We find that the correct hypercharge assignment of the standard model particles is reproduced for six viable models distinguished by different brane configurations. We investigate the third generation fermion mass relations and find that the correct low energy m_b/m_τ ratio can be obtained for b-τ Yukawa coupling equality at a string scale as low as M_S~10³ TeV. Received: 30 August 2005, Published online: 16 November 2005 PACS: 11.25.Wx, 11.25.Uv, 12.10.Kt     

Phase transitions of quasistationary states in the Hamiltonian Mean Field model

The out-of equilibrium dynamics of the Hamiltonian Mean Field (HMF) model is studied in presence of an externally imposed magnetic field h. Lynden-Bell’s theory of violent relaxation is revisited and shown to adequately capture the system dynamics, as revealed by direct Vlasov based numerical simulations in the limit of vanishing field. This includes the existence of an out-of-equilibrium phase transition separating magnetized and non magnetized phases. We also monitor the fluctuations in time of the magnetization, which allows us to elaborate on the choice of the correct order parameter when challenging the performance of Lynden-Bell’s theory. The presence of the field h removes the phase transition, as it happens at equilibrium. Moreover, regions with negative susceptibility are numerically found to occur, in agreement with the predictions of the theory.     

Size-induced appearance of ferroelectricity in thin antiferroelectric films

In the paper we consider size effects on phase transitions and polar properties of thin antiferroelectric films. We extend the phenomenological approach proposed by Kittel for thin films allowing for gradient (correlation) energy and depolarization field energy. Surface piezoelectric effect as well as misfit strain appear due to lattice constants mismatch between the film and its substrate. Direct variational method is used to derive the free energy with renormalized coefficients depending on the film thickness. Obtained free energy expression allows the calculation of phase diagrams and all electro-physical properties by a conventional minimization procedure. Approximate analytical expressions for the paraelectric–antiferroelectric–ferroelectric transition temperature dependences on film thickness, polarization gradient coefficient, and extrapolation lengths were obtained. The thickness dependence of the electric field critical value that causes antiferroelectric–ferroelectric phase transition was calculated. Under favorable conditions the antiferroelectric phase at first transforms into ferroelectric one and then into paraelectric phase with the decrease of the film thickness. Proposed theoretical consideration explains the experimental results obtained in antiferroelectric PbZrO₃ thin films.     

Mixed spin transverse Ising model with longitudinal random crystal field interactions

The effect of a longitudinal random crystal field interaction on the phase diagrams of the mixed spin transverse Ising model consisting of spin-1/2 and spin-1 is investigated within the finite cluster approximation based on a single-site cluster theory. In order to expand a cluster identity of spin-1, we transform the spin-1 to spin-1/2 representation containing Pauli operators. We derive the state equations applicable to structures with arbitrary coordination number N. The phase diagrams obtained in the case of a honeycomb lattice (N=3) and a simple-cubic lattice (N=6), are qualitatively different and examined in detail. We find that both systems exhibit a variety of interesting features resulting from the fluctuation of the crystal field interactions. Received: 13 February 1998 / Accepted: 17 March 1998     

Polarization-flip transition under electric field in BCCD

Three-axes elastic neutron scattering measurements demonstrate that the five-fold modulated phase (phase 1/5) of BCCD exhibits under electric field a phase transition without change of superlattice periodicity. Through the monitoring of high-order satellite diffraction peaks as a function of electric field and temperature, the competition between this phase and neighboring polar phases with other periods has been characterized. At a threshold electric field of about 20 kV/cm, a rather abrupt redistribution of the satellite intensities of phase 1/5 is observed, without change of the corresponding primary modulation wave vector ( ⅕). A quantitative analysis of these intensity variations confirms the earlier conjecture based on dielectric experiments that the modulation essentially changes from a non-polar sequence 5up5down ( <5>) of polarized z-perpendicular layers of basic semicells, to a polar sequence 6up4down ( <64>). The transition is caused by the flip of the average polarization of one of the interface layers, and can then be described as a bounded discrete motion of the wall separating positive and negative microdomains within the five-fold unit cell. This type of polarization-flip phase transition had been detected and characterized in one-dimensional theoretical models as generalized Frenkel-Kontorova models or spin chains with elastic couplings, but had not been anticipated in theoretical analyses of BCCD, for which other phenomenological or microscopic models (as the ANNNI model) have been considered adequate. Only recently and in view of the experimental results reported here, we demonstrated, using a general phenomenological displacive model, the possibility of this type of transition in systems as BCCD [Phys. Rev. B 62, 11418 (2000)]. Phase diagrams with spin-flip phase transitions yield very peculiar phase diagrams with a checkerboard topological structure and self-similar features. In particular, they may present special critical points as the so-called upsilon points [J. Statistical Phys. 62, 45 (1991)]. BCCD may be then the first experimental system where they could be observed. Received 20 September 2001     

Brane universes with Gauss-Bonnet-induced-gravity

The DGP brane world model allows us to get the observed late time acceleration via modified gravity, without the need for a “dark energy” field. This can then be generalised by the inclusion of high energy terms, in the form of a Gauss-Bonnet bulk. This is the basis of the Gauss-Bonnet-Induced-Gravity (GBIG) model explored here with both early and late time modifications to the cosmological evolution. Recently the simplest GBIG models (Minkowski bulk and no brane tension) have been analysed. Two of the three possible branches in these models start with a finite density “Big-Bang” and with late time acceleration. Here we present a comprehensive analysis of more general models where we include a bulk cosmological constant and brane tension. We show that by including these factors it is possible to have late time phantom behaviour.     

Diagrammar in classical scalar field theory

In this paper we analyze perturbatively a g?⁴classical field theory with and without temperature. In order to do that, we make use of a path-integral approach developed some time ago for classical theories. It turns out that the diagrams appearing at the classical level are many more than at the quantum level due to the presence of extra auxiliary fields in the classical formalism. We shall show that a universal supersymmetry present in the classical path-integral mentioned above is responsible for the cancelation of various diagrams. The same supersymmetry allows the introduction of super-fields and super-diagrams which considerably simplify the calculations and make the classical perturbative calculations almost “identical” formally to the quantum ones. Using the super-diagrams technique, we develop the classical perturbation theory up to third order. We conclude the paper with a perturbative check of the fluctuation-dissipation theorem.     

One-Loop Feynman Diagram Zeta-Functions in T > 0 Field Theory

The Matsubara sums of Euclidean finite-temperature (T>0) field theory, over discrete energy, express the nontrivial topology of cylindrical T>0 spacetime. We explore the possibility that an individual T>0 Feynman diagram can be identified as a special value of a ζ-function or other meromorphic function, whose existence depends on the cylindrical topology. (Here “meromorphic” refers to one or more complex variables in which analytic continuation is performed.) We prove that one-loop Feynman diagrams with 0, 1, 2, 3, … external lines do indeed have an associated ζ-function. This “Feynman diagram ζ-function” is by construction a convenient tool for the regularization (dimensional or analytic) of its diagram. But the true power of the diagram ζ-function approach shows up in the straightforward derivation they provide of exact high-T series expansions of the one-loop diagrams. All Feynman diagrams which are simple products of one-loop diagrams can be analysed conveniently in this way. Diagrams which involve overlapping loops are more difficult, and are only briefly touched upon here. Scalar fields are studied in this paper. Two sequels will deal with T>0 fields having spin, and field theory on toroidal spacetimes T^N×Eⁿ, which generalizes the considerations in this paper on T>0 spacetime S¹×Eⁿ.