Bianchi VI0 models in N=2, D=5 supergravity

We investigate Bianchi VI₀ cosmological models containing two interacting scalar fields. These models are derived from a dimensional reduction of theN=2,D=5 supergravity theory. Exact solutions are found and the existence of singularities for them is considered.     

Unitarity of rationalN = 2 superconformal theories

We demonstrate that all rational models of theN = 2 super Virasoro algebra are unitary. Our arguments are based on three different methods: we determine Zhu’s algebraA(H₀) (for which we give a physically motivated derivation) explicitly for certain theories, we analyse the modular properties of some of the vacuum characters, and we use the coset realisation of the algebra in terms ofsu(2) and two free fermions. Some of our arguments generalise to the Kazama-Suzuki models indicating that all rationalN = 2 supersymmetric models might be unitary.     

A relation betweenD=10, D=26 andD=32: Analysing the spacetime content of string-type field theories

A detailed analysis of the spacetime content of string-type field theories is presented. We rigorously explain the appearance ofD=10 andD=26, and argue that they are naturally contained inD=32. Our results suggest a new way to the compactification of theD=10 fermionic string and possible new (fermionic) models forD=4, D=6 andD=18. Some connected aspects are also discussed.     

A Trinomial Analogue of Bailey's Lemma and N = 2 Superconformal Invariance

We propose and prove a trinomial version of the celebrated Bailey's lemma. As an application we obtain new fermionic representations for characters of some unitary as well as nonunitary models of N= 2 superconformal field theory (SCFT). We also establish interesting relations between N= 1 and N= 2 models of SCFT with central charges and . A number of new mock theta function identities are derived. Dedicated to Dora Bitman on her 70th birthday Received: 8 March 1997 / Accepted: 29 June 1997     

The two-dimensional,N=2 Wess-Zumino model on a cylinder

We construct a family of supersymmetric, two-dimensional quantum field models. We establish the existence of the HamiltonianH and the superchargeQ as self-adjoint operators. We establish the ultraviolet finiteness of the model, independent of perturbation theory. We develop functional integral representations of the heat kernel which are useful for proving estimates in these models. In a companion paper [1] we establish an index theorem forQ, an infinite dimensional Dirac operator on loop space. This paper and, another related one [2], provide the technical justification for our claim thatQ is Fredholm, and for our computation of its index by a homotopy onto quantum mechanics.Supported in part by the National Science Foundation under Grant DMS/PHY 86-45122Hertz Foundation Graduate Fellow     

N = 4 mechanics,WDVV equations and polytopes

N = 4 superconformal n-particle quantum mechanics on the real line is governed by two prepotentials, U and F, which obey a system of partial nonlinear differential equations generalizing the Witten—Dijkgraaf—Verlinde—Verlinde (WDVV) equation for F. The solutions are encoded by the finite Coxeter systems and certain deformations thereof, which can be encoded by particular polytopes. We provide A _n and B ₃ examples in some detail. Turning on the prepotential U in a given F background is very constrained for more than three particles and nonzero central charge. The standard ansatz for U is shown to fail for all finite Coxeter systems. Three-particle models are more flexible and based on the dihedral root systems.     

Renormalizable N = 2 Supersymmetric Gauge Theories

Renormalizable supersymmetric models of matter multiplets coupled to a Yang Mills multiplet are studied in the conventional N = 2 superspace. It is found that a consistent formulation of the Feynman rules in superspace requires the introduction of a compensator superfield in the matter sector. If the quantization is performed within the background superfield approach, the use of the compensator is confined to the quantum corrections. The ensuing ghost structure is analyzed and the non-renormalization beyond one-loop is demonstrated. We report an N = 2 superfield calculation of the one-loop β-function via the supercurrent anomaly and thereby derive as a byproduct the finiteness criterion for N = 2 non-Abelian gauge theories.     

On the Poisson-Lie T-duality in two-dimensional N=2 superconformal field theories

A supersymmetric generalization of the Poisson-Lie T-duality transformation is proposed. It is shown that N=2 superconformal two-dimensional WZNW models possess natural Poisson-Lie symmetry, which makes it possible to construct Poisson-Lie T-dual σ models. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 12, 823–828 (25 December 1996)     

On classification ofN=2 supersymmetric theories

We find a relation between the spectrum of solitons of massiveN=2 quantum field theories ind=2 and the scaling dimensions of chiral fields at the conformal point. The condition that the scaling dimensions be real imposes restrictions on the soliton numbers and leads to a classification program for symmetricN=2 conformal theories and their massive deformations in terms of a suitable generalization of Dynkin diagrams (which coincides with the A-D-E Dynkin diagrams for minimal models). The Landau-Ginzburg theories are a proper subset of this classification. In the particular case of LG theories we relate the soliton numbers with intersection of vanishing cycles of the corresponding singularity; the relation between soliton numbers and the scaling dimensions in this particular case is a well known application of Picard-Lefschetz theory.     

Renormalisation group for depinning transition ind=2 ising models

We develop a position space renormalisation group (RG) method to study generalised depinning transition in two-dimensional Ising models. The treatment encompasses (i) the original model for depinning invented by Abraham, (ii) generalised depinning model, (iii) nonuniversal behaviour near the internal line of defects and (iv) surface and interface behaviour. The phase diagrams and the thermodynamic functions over the whole range of temperatures are obtained. The agreement with exact results (when available) is quite satisfactory.     

<Emphasis Type="Italic">C</Emphasis>-field Cosmological Models with Variable <Emphasis Type="Italic">G</Emphasis> in FRW Space–Time

C-field cosmological models based on Hoyle-Narlikar theory with variable gravitational constant G in the frame work of FRW (Friedmann-Robertson-Walker) space–time for positive and negative curvatures are investigated. To get the deterministic solutions in terms of cosmic time t, we have assumed G=R ⁿ and discussed for n=−1, −2, R being scalar factor. In both the cases, creation field C increases with time, the gravitational constant G and matter density (ρ) decrease with time in the model (21). In the model (41) G decreases with time and matter density (ρ) is constant. The other physical aspects of the models are also discussed.     

The T cc = DD* Molecular State

We show that the molecule-like configuration of DD* enables weak binding with two realistic potential models (Bhaduri and Grenoble AL1). Three-body forces may increase the binding and strengthen the cc diquark configuration. As a signature we propose the branching ratio between radiative and pionic decay.     

PAC analysis of defect motion by Blume's stochastic model forI=5/2 electric quadrupole interactions

Using Blume's stochastic model and the approach of Winkler and Gerdau, we have computed time-dependent effects on perturbed angular correlation (PAC) spectra due to defect motion in solids in the case ofI=5/2 electric quadrupole interactions. We report detailed analysis for a family of simple models: “XYZ+Z” models, in which the symmetry axis of an axial EFG is allowed to fluctuate among orientations alongx, y, andz axes, and a static axial EFG oriented along thez axis is added to the fluctuating EFGs. When the static EFG is zero, this model is termed the “XYZ” model. Approximate forms are given forG ₂(t) in the slow and rapid fluctuation regimes, i.e. suitable for the low and high temperature regions, respectively. Where they adequately reflect the underlying physical processes, these expressions allow one to fit PAC data for a wide range of temperatures and dopant concentrations to a single model, thus increasing the uniqueness of the interpretation of the defect properties. Application of the models is illustrated with data from a PAC study of tetragonal zirconia.     

Disappearing cosmological constant in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

For higher-derivative f(R) gravity, where R is the Ricci scalar, a class of models is proposed, which produce viable cosmology different from the ACDM at recent times and satisfy cosmological, Solar System, and laboratory tests. These models have both flat and de Sitter spacetimes as particular solutions in the absence of matter. Thus, a cosmological constant is zero in a flat spacetime, but appears effectively in a curved one for sufficiently large R. A “smoking gun” for these models would be a small discrepancy in the values of the slope of the primordial perturbation power spectrum determined from galaxy surveys and CMB fluctuations. On the other hand, a new problem for dark energy models based on f(R) gravity is pointed out, which is connected with the possible overproduction of new massive scalar particles (scalarons) arising in this theory in the very early Universe. The text was submitted by the author in English.     

A phenomenological analysis of the longitudinal structure function at small <Emphasis Type="Italic">x</Emphasis> and low <Emphasis Type="Italic">Q</Emphasis><Superscript>2</Superscript>

The longitudinal structure function in deep-inelastic scattering is one of the observables from which the gluon distribution can be unfolded. Consequently, this observable can be used to constrain the QCD dynamics at small x. In this work we compare the predictions of distinct QCD models with the recent experimental results for F _L(x,Q ²) at small x and low Q ² obtained by the H1 Collaboration. We focus mainly on the color dipole approach, selecting those models which include saturation effects. Such models are suitable at this kinematical region and also resum a wide class of higher-twist contributions to the observables. Therefore, we investigate the influence of these corrections to F _L in the present region of interest.Received: 23 June 2004, Revised: 13 July 2004, Published online: 14 September 2004     

Flavour-changing neutral currents in models with extra<Emphasis Type="Italic">Z′</Emphasis> boson

New neutral gauge bosonsZ′ are the features of many models addressing the physics beyond the standard model. Together with the existence of new neutral gauge bosons, models based on extended gauge groups (rank > 4) often predict new charged fermions also. A mixing of the known fermions with new states, with exotic weak-isospin assignments (left-handed singlets and right-handed doublets) will induce tree-level flavour-changing neutral interactions mediated byZ exchange, while if the mixing is only with new states with ordinary weak-isospin assignments, the flavour-changing neutral currents are mainly due to the exchange of the new neutral gauge bosonZ′. We review flavour-changing neutral currents in models with extraZ′ boson. Then we discuss some flavour-changing processes forbidden in the standard model and new contributions to standard model processes.     

Flavored surface defects in 4d $$\mathcal{N}=1$$ N = 1 SCFTs

We discuss supersymmetric surface defects in compactifications of six-dimensional minimal conformal matter of types SU(3) and SO(8) to four dimensions. The relevant field theories in four dimensions are \(\mathcal{N}=1\) quiver gauge theories with SU(3) and SU(4) gauge groups, respectively. The defects are engineered by giving space-time-dependent vacuum expectation values to baryonic operators. We find evidence that in the case of SU(3) minimal conformal matter, the defects carry SU(2) flavor symmetry which is not a symmetry of the four-dimensional model. The simplest case of a model in this class is SU(3) SQCD with nine flavors, and thus the results suggest that this admits natural surface defects with SU(2) flavor symmetry. We analyze the defects using the superconformal index and derive analytic difference operators introducing the defects into the index computation. The duality properties of the four-dimensional theories imply that the index of the models is a kernel function for such difference operators. In turn, checking the kernel property constitutes an independent check of the dualities and the dictionary between six- dimensional compactifications and four-dimensional models.

     

On the Complete Classification of Unitary <Emphasis Type="Italic">N</Emphasis> = 2 Minimal Superconformal Field Theories

Aiming at a complete classification of unitary N = 2 minimal models (where the assumption of space-time supersymmetry has been dropped), it is shown that each modular invariant candidate partition function of such a theory is indeed the partition function of a fully-fledged unitary N = 2 minimal model, subject to the assumptions that orbifolding is a ‘physical’ process and that the space-time supersymmetric A{\mathcal{A}} -D{\mathcal{D}} -E{\mathcal{E}} models are physical. A family of models constructed via orbifoldings of either the diagonal model or of the space-time supersymmetric exceptional models then demonstrates that there exists a unitary N = 2 minimal model for every one of the allowed partition functions in the list obtained from Gannon’s work (Gannon in Nucl Phys B 491:659–688, 1997).     

The Z = 82 shell closure in neutron-deficient Pb isotopes

Recent mass measurements show a substantial weakening of the binding-energy difference δ_2p(Z, N) = E(Z - 2, N) - 2E(Z, N) + E(Z + 2, N) in the neutron-deficient Pb isotopes. As δ_2p is often attributed to the size of the proton magic gap, it might be speculated that reduction in δ_2p is related to a weakening of the spherical Z = 82 shell. We demonstrate that the observed trend is described quantitatively by self-consistent mean-field models in terms of deformed ground states of Hg and Po isotopes. Received: 25 October 2001 / Accepted: 28 February 2002