Matryoshka of Special Democratic Forms

Special p-forms are forms which have components ${\varphi_{\mu_1\dots\mu_p}}Special p-forms are forms which have components j_m1...mp{\varphi_{\mu_1\dots\mu_p}} equal to +1, −1 or 0 in some orthonormal basis. A p-form j ? L^p\mathbbR^d{\varphi\in \Lambda^p\mathbb{R}^d} is called democratic if the set of nonzero components {j_m1...mp}{\{\varphi_{\mu_1\dots\mu_p}\}} is symmetric under the transitive action of a subgroup of O(d,\mathbbZ){{\rm O}(d,\mathbb{Z})} on the indices {1, . . . , d}. Knowledge of these symmetry groups allows us to define mappings of special democratic p-forms in d dimensions to special democratic P-forms in D dimensions for successively higher P ≥ p and D ≥ d. In particular, we display a remarkable nested structure of special forms including a U(3)-invariant 2-form in six dimensions, a G₂-invariant 3-form in seven dimensions, a Spin(7)-invariant 4-form in eight dimensions and a special democratic 6-form Ω in ten dimensions. The latter has the remarkable property that its contraction with one of five distinct bivectors, yields, in the orthogonal eight dimensions, the Spin(7)-invariant 4-form. We discuss various properties of this ten dimensional form.     

Toda lattice hierarchy and generalized string equations

String equations of thep ^th generalized Kontsevich model and the compactifiedc=1 string theory are re-examined in the language of the Toda lattice hierarchy. As opposed to a hypothesis postulated in the literature, the generalized Kontsevich model atp=–1 does not coincide with thec=1 string theory at selfdual radius. A broader family of solutions of the Toda lattice hierarchy including these models is constructed, and shown to satisfy generalized string equations. The status of a variety ofc1 string models is discussed in this new framework.     

Characteristic cohomology ofp-form gauge theories

The characteristic cohomologyH ^k _char(d) for an arbitrary set of freep-form gauge fields is explicitly worked out in all form degreesk < n — 1, wheren is the spacetime dimension. It is shown that this cohomology is finite-dimensional and completely generated by the forms dual to the field strengths. The gauge invariant characteristic cohomology is also computed. The results are extended to interactingp-form gauge theories with gauge invariant interactions. Implications for the BRST cohomology are mentioned.     

p t -Multiplicity correlations in a multi-pomeron-exchange model with string collective effects

The 〈p _t 〉N _ch - N _ch correlations experimentally observed in the central rapidity region in pp and p collisions, in a wide energy range from the ISR to Tevatron, are described in the framework of a multi-Pomeron exchange model in which string collectivity has been included in an effective way. Three parameters are obtained from the fit to data: the string tension, the average number of particles per string, and a parameter which effectively introduces string collective effects. The model successfully reproduces the rise of 〈p _t 〉 of charged particles, the flattening with growing rapidity density of charged particles and with the collision energy, and the negative p _t -N _ch correlation at low energies. The string tension and the average number of particles per string are energy independent, while the parameter that includes effectively string collective effects shows a smooth increasing behavior with energy. The text was submitted by the authors in English.     

Connections on Naturally Reductive Spaces,Their Dirac Operator and Homogeneous Models in String Theory

 Given a reductive homogeneous space M=G/H endowed with a naturally reductive metric, we study the one-parameter family of connections ∇ ^t joining the canonical and the Levi-Civita connection (t=0, 1/2). We show that the Dirac operator D ^t corresponding to t=1/3 is the so-called ``cubic' Dirac operator recently introduced by B. Kostant, and derive the formula for its square for any t, thus generalizing the classical Parthasarathy formula on symmetric spaces. Applications include the existence of a new G-invariant first order differential operator on spinors and an eigenvalue estimate for the first eigenvalue of D <sup>1/3</sup>. This geometric situation can be used for constructing Riemannian manifolds which are Ricci flat and admit a parallel spinor with respect to some metric connection ∇ whose torsion T≠ 0 is a 3-form, the geometric model for the common sector of string theories. We present some results about solutions to the string equations and a detailed discussion of a 5-dimensional example. Received: 19 February 2002 / Accepted: 26 August 2002 Published online: 22 November 2002 RID="*" ID="*" This work was supported by the SFB 288 ``Differential geometry and quantum physics' of the Deutsche Forschungsgemeinschaft and the Max-Planck Society.     

Conformal Maps and Integrable Hierarchies

We show that conformal maps of simply connected domains with an analytic boundary to a unit disk have an intimate relation to the dispersionless 2D Toda integrable hierarchy. The maps are determined by a particular solution to the hierarchy singled out by the conditions known as “string equations”. The same hierarchy locally solves the 2D inverse potential problem, i.e., reconstruction of the domain out of a set of its harmonic moments. This is the same solution which is known to describe 2D gravity coupled to c= matter. We also introduce a concept of the τ-function for analytic curves. Received: 20 December 1999/ Accepted: 2 March 2000     

Total cross sections of hadron interactions at high energies in a model with low number of constituents

We consider a quantum chromodynamics (QCD)-hadron interaction model in which the gluon density is low in the initial state wave function in rapidity space and real hadrons are produced from color string decay. In this model, the behavior of the total cross sections of pp, p$ \bar p $ \bar p , π^± p, K ^± p, γp, and γγ interactions is well described. The value of the proton-proton total cross section under the energy of the Large Hadron Collider (LHC) is predicted.     

String model description of polarisation and angular distributions in ¯pp → ¯ΛΛ at low energies

The observed polarisation of Λ hyperons from the inclusive pA → ΛX reaction at high energies has previously been well described within the Lund string model through polarised sˉs quark pair production in the string breaking hadronisation process. This model is here applied to the exclusive ˉpp → ˉΛΛ reaction at low energies and compared to available data sets down to an incident-beam momentum of 1.835 GeV/c. This required an extension of the diquark scattering model to involve three components: an isotropic part relevant close to the threshold, a spectator part and a forward-scattering part as in pA → ΛX at high energies. The observed angular distributions are then reproduced and, for momentum transfers above | t'| = 0.2 GeV², agreement with the measured polarisation is also obtained. Received: 2 April 2002 / Accepted: 24 July 2002 / Published online: 3 December 2002 RID="a" ID="a"Present address: Department of Neutron Research, Uppsala University, Box 525, S-75120 Uppsala, Sweden; e-mail: Stephan.Pomp@tsl.uu.se. RID="b" ID="b"Present address: ESRF, F-38043 Grenoble, France. Communicated by A. Sch?fer     

CMS ridge effect at LHC as a manifestation of bremsstrahlung of gluons off quarks accelerated in a strong color field

The recently reported effect of long-range near-side angular correlations at LHC occurs for large multiplicities of particles with 1 GeV<p _T <3 GeV. To understand the effect several possibilities have been discussed. In the letter we propose a simple qualitative mechanism which corresponds to gluon bremsstrahlung of quarks moving with acceleration defined by the string tension. The smallness of azimuthal angle difference Δφ along with large Δη at large multiplicities in this interval of p _T are natural in this mechanism. The mechanism predicts also bremsstrahlung photons with mean values of p _T ≈2.9 and 0.72 GeV.     

Plane Symmetric String Cosmological Model in Modified Theory of General Relativity

It is shown that homogeneous plane symmetric string cosmological model for Takabayasi string i.e. ρ=(1+ω)λ does not exist in Barber’s second self creation theory. Further it is found that the string cosmological model in this theory exist only when ω=0. Therefore model for ρ=λ (geometric string) is constructed. Some physical and geometrical properties of the model are discussed.     

Superstrings in Curved Ramond-Ramond Backgrounds

We discuss the main issues related to understanding closed string spectrum in Ramond-Ramond backgrounds on the example of AdS₅ × S ⁵ and and its special limit – the maximally supersymmetric plane-wave background with constant null 5-form field strength. As we describe, in the latter case the spectrum can be found explicitly. We compare the plane-wave string spectrum with the expected form of the light-cone gauge spectrum of the AdS₅ × S ⁵ superstring and comment on the tensionless string limit.     

BRST analysis of topologically massive gauge theory: novel observations

A dynamical non-Abelian 2-form gauge theory (with B∧F term) is endowed with the “scalar” and “vector” gauge symmetry transformations. In our present endeavor, we exploit the latter gauge symmetry transformations and perform the Becchi–Rouet–Stora–Tyutin (BRST) analysis of the four (3+1)-dimensional (4D) topologically massive non-Abelian 2-form gauge theory. We demonstrate the existence of some novel features that have, hitherto, not been observed in the context of BRST approach to 4D (non-)Abelian 1-form as well as Abelian 2-form and 3-form gauge theories. We comment on the differences between the novel features that emerge in the BRST analysis of the “scalar” and “vector” gauge symmetries.     

The Variational Principle for a Class of Asymptotically Abelian C*-Algebras

Let (A,α) be a C^*-dynamical system. We introduce the notion of pressure P _α(H) of the automorphism α at a self-adjoint operator H∈A. Then we consider the class of AF-systems satisfying the following condition: there exists a dense α-invariant *-subalgebra ? of A such that for all pairs a,b∈? the C^*-algebra they generate is finite dimensional, and there is p=p(a,b)∈ℕ such that [α ^j (a),b]= 0 for |j|≥p. For systems in this class we prove the variational principle, i.e. show that P _α(H) is the supremum of the quantities h _φ(α) −φ(H), where h _φ(α) is the Connes–Narnhofer–Thirring dynamical entropy of α with respect to the α-invariant state φ. If H∈A, and P _α(H) is finite, we show that any state on which the supremum is attained is a KMS-state with respect to a one-parameter automorphism group naturally associated with H. In particular, Voiculescu's topological entropy is equal to the supremum of h _φ(α), and any state of finite maximal entropy is a trace. Received: 19 April 2000 / Accepted: 14 June 2000     

String cosmology in LRS Bianchi type-II dusty Universe with time-decaying vacuum energy density Λ

A model of a cloud formed by massive strings is used as a source of LRS Bianchi type-II with time-decaying vacuum energy density Λ. To construct string cosmological models, we have used the energy–momentum tensor for such strings as formulated by Letelier (1983). The high nonlinear field equations have been solved for two types of strings: (i) massive string and (ii) Nambu string. The expansion θ in the model is assumed to be proportional to the shear σ. This condition leads to A = βB ^m , where A and B are the metric coefficients, m is a constant and β is an integrating constant. Our models are in accelerating phase which is consistent with the recent observations of supernovae type-Ia. The physical and geometrical behaviour of these models are also discussed.     

On conformal Killing 2-form of the electromagnetic field

Let D:C^∞Λ^pM→C^∞(T^*MΛ^pM) be the first order linear differential operator on an n-dimensional (1≤p≤n−1) pseudo-Riemannian manifold (M,g). We have by the representation theory of orthogonal group, that the tangent bundle of this operation decomposes into the orthogonal and irreducible sum of forms of degree p+1 (which gives the exterior differential d), the forms of degree p−1 (defining the codifferential d^*) and the trace-free part of the partial symmetrization (the corresponding first order operator is denoted by D). The general forms in the kernel of D are closely related to conformal Killing vector fields, called conformal Killing p-forms, while those in kernel of d are called closed conformal Killing p-forms or, according to another terminology, planar p-forms. In particular an arbitrary planar 1-form ω is dual (by g) to the special concircular vector field ξ. We consider some local properties for the closed conformal Killing p-forms. As an application we present examples of decomposition into irreducible components for the electromagnetic field 2-form ω and its covariant derivative in four-dimensional space–time. In particular, we prove that the energy–momentum tensor T of the electromagnetic field is a symmetric conformal Killing tensor if the electromagnetic field 2-form ω is a conformal Killing form.     

Investigation of scaling laws as applied to the gas discharge in the case of a barrier-discharge-excited Kr/CCl<Subscript>4</Subscript> mixture

The electrical and luminescent characteristics of a barrier-discharge lamp filled with a Kr/CCl₄ (150: 1) mixture are experimentally studied versus the value of pd, which varies in the range (7.6–14) × 10³ Pa cm. When simulating the gas discharge using similarity parameters, the following relationships are fulfilled: for pd = const (p is the pressure, d is the interelectrode distance), the pulse duration and the mean current density are τ _j ∼ 1/p and 〈j〉 ∼ p; the surface charge density on the electrodes, σ ∼ const; the duration of the UV radiation pulse and the efficiency of UV radiation due to a KrCl* (222 nm) exciplex, τ_rad ∼ 1/p and η ∼ p ². The maximal radiation efficiency achieved in the experiments is about 13%. Deviations from the similarity laws for the gas discharge are related to the filamentary form of the observed discharge. Qualitative analysis indicates that similarity laws may be fulfilled for such a form of discharge as well but locally, within a single filament.     

Abelian 2-form gauge theory: superfield formalism

We derive the off-shell nilpotent Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetry transformations for all the fields of a free Abelian 2-form gauge theory by exploiting the geometrical superfield approach to the BRST formalism. The above four (3+1)-dimensional (4D) theory is considered on a (4, 2)-dimensional supermanifold parameterized by the four even spacetime variables x ^μ (with μ=0,1,2,3) and a pair of odd Grassmannian variables θ and (with ). One of the salient features of our present investigation is that the above nilpotent (anti-) BRST symmetry transformations turn out to be absolutely anticommuting due to the presence of a Curci–Ferrari (CF) type of restriction. The latter condition emerges due to the application of our present superfield formalism. The actual CF condition, as is well known, is the hallmark of a 4D non-Abelian 1-form gauge theory. We demonstrate that our present 4D Abelian 2-form gauge theory imbibes some of the key signatures of the 4D non-Abelian 1-form gauge theory. We briefly comment on the generalization of our superfield approach to the case of Abelian 3-form gauge theory in four, (3+1), dimensions of spacetime.     

String cosmology in Bianchi I space-time

Some cosmological solutions of massive strings are obtained in Bianchi I space-time following the techniques used by Letelier and Stachel. A class of solutions corresponds to string cosmology associated with/without a magnetic field and the other class consists of pure massive strings, obeying the Takabayashi equation of stateρ=(1+W)λ.     

Shock profiles for the asymmetric simple exclusion process in one dimension

The asymmetric simple exclusion process (ASEP) on a one-dimensional lattice is a system of particles which jump at ratesp and 1-p (herep > 1/2) to adjacent empty sites on their right and left respectively. The system is described on suitable macroscopic spatial and temporal scales by the inviscid Burgers’ equation; the latter has shock solutions with a discontinuous jump from left density ρ- to right density ρ+, ρ-< ρ +, which travel with velocity (2p−1 )(1−ρ₊−p ₋). In the microscopic system we may track the shock position by introducing a second class particle, which is attracted to and travels with the shock. In this paper we obtain the time-invariant measure for this shock solution in the ASEP, as seen from such a particle. The mean density at lattice siten, measured from this particle, approachesp _± at an exponential rate asn→ ±∞, witha characteristic length which becomes independent ofp when . For a special value of the asymmetry, given byp/(1−p)=p ₊(1−p ₋)/p ₋(1−p ₊), the measure is Bernoulli, with densityρ ₋ on the left andp ₊ on the right. In the weakly asymmetric limit, 2p−1 → 0, the microscopic width of the shock diverges as (2p+1)^-1. The stationary measure is then essentially a superposition of Bernoulli measures, corresponding to a convolution of a density profile described by the viscous Burgers equation with a well-defined distribution for the location of the second class particle.     

Λ-Baryon production in π ± N interactions

The process of Λ-baryon production in πp collisions is considered. The contribution of the string-junction mechanism to the strange-baryon production in meson-baryon scattering is analyzed. The results of numerical calculations in the framework of the quark-gluon string model are in reasonable agreement with the data. The text was submitted by the authors in English.