Regularization by higher derivatives and quantum correction for <Emphasis Type="Italic">N</Emphasis> = 1 supersymmetric theories

Some results of regularization by higher covariant derivatives used for investigation of the structure of quantum corrections in N = 1 supersymmetric theories are summarized in the present work. In particular, it is demonstrated that all integrals determining the Hell-Mann-Low functions in supersymmetric theories are integrals of total derivatives. As a consequence, in the N = 1 supersymmetric theories there exists an identity for the Green’s functions which follows from none of the symmetry theories known thus far. The problem of obtaining the exact β-function by the methods of perturbation theory is discussed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 5–35, May, 2008.     

<Emphasis Type="Italic">N</Emphasis> = 4 supersymmetric Eguchi-Hanson sigma model in <Emphasis Type="Italic">d</Emphasis> = 1

We show that it is possible to construct a supersymmetric mechanics with four supercharges possessing not conformally flat target space. A general idea of constructing such models is presented. A particular case with Eguchi-Hanson target space is investigated in detail: we present the standard and quotient approaches to get the Eguchi-Hanson model, demonstrate their equivalence, give a full set of nonlinear constraints, study their properties and give an explicit expression for the target space metric. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Decay properties of <Emphasis Type="Italic">N</Emphasis>∼<Emphasis Type="Italic">Z</Emphasis> nuclei

By using heavy-ion induced fusion-evaporation reactions at the on-line mass separator of GSI, the decay properties of neutron-deficient isotopes between ⁵⁶Ni and ¹⁰⁰Sn were investigated. The experimental results will be presented and discussed in comparison with model predictions.     

Glueballs,gluerings, and gluestars in the <Emphasis Type="Italic">d</Emphasis> = 2 + 1 <Emphasis Type="Italic">SU</Emphasis>(<Emphasis Type="Italic">N</Emphasis>) gauge theory

The 3d gluodynamics which governs the large-T quark—gluon plasma is studied in the framework of the field correlator method. Field correlators and spacial string tension are derived through the gluelump Green’s functions. The glueball spectrum is calculated both in C = −1 as well as in C = +1 sectors, and multigluon bound states in the form of “gluon rings” and “gluon stars” are computed explicitly. Good overall agreement with available lattice data is observed. The text was submitted by the author in English.     

<Emphasis Type="Italic">N</Emphasis> = 1 Supersymmetric Sigma Model with Boundaries,I

 We study an N=1 two-dimensional non-linear sigma model with boundaries representing, e.g., a gauge fixed open string. We describe the full set of boundary conditions compatible with N=1 superconformal symmetry. The problem is analyzed in two different ways: by studying requirements for invariance of the action, and by studying the conserved supercurrent. We present the target space interpretation of these results, and identify the appearance of partially integrable almost product structures. Received: 27 November 2001 / Accepted: 16 August 2002 Published online: 19 December 2002 Acknowledgements. We are grateful to Ingemar Bengtsson and Andrea Cappelli for discussions and comments. MZ would like to thank the ITP, Stockholm University, where part of this work was carried out. UL acknowledges support in part by EU contract HPNR-CT-2000-0122 and by NFR grant 650-1998368. Communicated by R.H. Dijkgraaf     

Reduced expression of <Emphasis Type="Italic">TAC1</Emphasis>, <Emphasis Type="Italic">PENK</Emphasis> and <Emphasis Type="Italic">SOCS2</Emphasis> in <Emphasis Type="Italic">Hcrtr-2</Emphasis> mutated narcoleptic dog brain

Background  

Narcolepsy causes dramatic behavioral alterations in both humans and dogs, with excessive sleepiness and cataplexy triggered by emotional stimuli. Deficiencies in the hypocretin system are well established as the origin of the condition; both from studies in humans who lack the hypocretin ligand (HCRT) and in dogs with a mutation in hypocretin receptor 2 (HCRTR2). However, little is known about molecular alterations downstream of the hypocretin signals.     

Topological Solitons in the <Emphasis Type="Italic">CP</Emphasis><Superscript><Emphasis Type="Italic">N</Emphasis></Superscript> Model

We investigate the solitons in the CP ^N model in terms of the decomposition of gauge potential. Based on the φ-mapping topological current theory, the charge and position of solitons is determined by the properties of the typical component. Furthermore, the motion and the bifurcation of multi-soliton is discussed. And the knotted solitons in high dimension is explored also.     

Quantum teleportation of an unknown <Emphasis Type="Italic">N</Emphasis>-Qubit W-Like state

Magnetoresistance is studied in a strongly correlated 2D electron system in Si in the critical regime in the close vicinity of the 2D metal-insulator transition. Our data are self-consistently compared with solutions of two equations of the crossover renormalization group theory, which describes temperature evolutions of the resistivity and interaction parameters for 2D electron systems. Good agreement is found between the ρ(T, B _∥) data and the renormalization group theory in a wide range of the in-plane fields, 0–2.1 T. This agreement supports the interpretation of the observed 2D MIT as the true quantum phase transition. The text was submitted by the authors in English.     

Large <Emphasis Type="Italic">N</Emphasis> Expansion of <Emphasis Type="Italic">q</Emphasis>-Deformed Two-Dimensional Yang-Mills Theory and Hecke Algebras

We derive the q-deformation of the chiral Gross-Taylor holomorphic string large N expansion of two dimensional SU(N) Yang-Mills theory. Delta functions on symmetric group algebras are replaced by the corresponding objects (canonical trace functions) for Hecke algebras. The role of the Schur-Weyl duality between unitary groups and symmetric groups is now played by q-deformed Schur-Weyl duality of quantum groups. The appearance of Euler characters of configuration spaces of Riemann surfaces in the expansion persists. We discuss the geometrical meaning of these formulae.     

The determination of <Emphasis Type="Italic">α</Emphasis><Subscript><Emphasis Type="Italic">S</Emphasis></Subscript> from <Emphasis Type="Italic">τ</Emphasis> decays revisited

We revisit the determination of α _S (m _τ ²) using a fit to inclusive τ hadronic spectral moments in light of (1) the recent calculation of the fourth-order perturbative coefficient K ₄ in the expansion of the Adler function, (2) new precision measurements from BABAR of e⁺e⁻ annihilation cross sections, which decrease the uncertainty in the separation of vector and axial-vector spectral functions, and (3) improved results from BABAR and Belle on τ branching fractions involving kaons. We estimate that the fourth-order perturbative prediction reduces the theoretical uncertainty, introduced by the truncation of the series, by 20% with respect to earlier determinations. We discuss to some detail the perturbative prediction of two different methods: fixed-order perturbation theory (FOPT) and contour-improved perturbative theory (CIPT). The corresponding theoretical uncertainties are studied at the τ and Z mass scales. The CIPT method is found to be more stable with respect to the missing higher order contributions and to renormalization scale variations. It is also shown that FOPT suffers from convergence problems along the complex integration contour. Nonperturbative contributions extracted from the most inclusive fit are small, in agreement with earlier determinations. Systematic effects from quark-hadron duality violation are estimated with simple models and found to be within the quoted systematic errors. The fit based on CIPT gives α _S (m _τ ²)=0.344±0.005±0.007, where the first error is experimental and the second theoretical. After evolution to M _Z we obtain α _S (M _Z ²)=0.1212±0.0005±0.0008±0.0005, where the errors are respectively experimental, theoretical and due to the evolution. The result is in agreement with the corresponding N³LO value derived from essentially the Z width in the global electroweak fit. The α _S (M _Z ²) determination from τ decays is the most precise one to date.     

GaSe<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript><Emphasis Type="Italic">S</Emphasis><Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> solid solutions

The most probable parameters of the pure, doped, and mixed GaSe_1−xS_x (x ≤ 0.4) crystals (solid solutions) are presented together with the results of investigations of their crystal structure and defects, optical and mechanical properties, and damage thresholds. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 35–40, June, 2007.     

On the Dirac eigenvalues as observables of the on-shell <Emphasis Type="Italic">N</Emphasis> = 2<Emphasis Type="Italic">D</Emphasis> = 4 Euclidean supergravity

We generalize previous works on the Dirac eigenvalues as dynamical variables of Euclidean gravity and N =1 D = 4 supergravity to on-shell N = 2 D = 4 Euclidean supergravity. The covariant phase space of the theory is defined as the space of the solutions of the equations of motion modulo the on-shell gauge transformations. In this space we define the Poisson brackets and compute their value for the Dirac eigenvalues.      

Mixed symmetry states and isospin excitation in <Emphasis Type="Italic">N</Emphasis> = <Emphasis Type="Italic">Z</Emphasis> nucleus <Superscript>52</Superscript>Fe

The interacting boson model with isospin (IBM-3) was applied to study the band structure and electromagnetic transition properties of the low-lying states in the even-even N = Z nucleus ⁵²Fe. The isospin excitation states with T = 0, 1 and 2 were identified, and compared with the available data. The study shows that the 2₃⁺ state is the lowest mixed symmetry state in ⁵²Fe. The excitation energy of the second 0₂⁺ state with T = 0 in nucleus ⁵²Fe was identified. The model calculations with the data show a reasonably good agreement. Supported by the National Natural Science Foundation of China (Grant Nos. 10765001 and 10547003), the Natural Science Foundation of Inner Mongolian Autonomous Region of China (Grant No. 200607010111), and the Scientific Research Fund of Inner Mongolian Education Bureau (Grant Nos. NJZY07155 and NJZY07153)     

A (<Emphasis Type="Italic">t</Emphasis>,<Emphasis Type="Italic">n</Emphasis>)-Threshold Scheme of Multi-party Quantum Group Signature with Irregular Quantum Fourier Transform

A novel (t,n)-threshold scheme for the multi-party quantum group signature is proposed based on the irregular quantum Fourier transform, in which every t-qubit quantum message needs n participants to generate the quantum group signature. All the quantum operation gates in the quantum circuit can be distributed and arranged randomly in the irregular QFT algorithm, which can increase the von Neumann entropy of the signed quantum message and the randomicity of the quantum signature generation significantly. The generation and verification of the quantum group signature can be both performed in quantum circuits with the parallel algorithm. Security analysis shows that an available and legal quantum (t,n)-threshold group signature can be achieved.     

<Emphasis Type="Italic">N</Emphasis> = 1, 2 supersymmetric non-local gas equation

In this paper we study the supersymmetrization of the N = 1 and N = 2 nonlocal gas equation. We show that this system is bi-Hamiltonian. While the N = 1 supersymmetrization allows the hierarchy of equations to be extended to negative orders (local equations), we argue that this is not the case for the N = 2 supersymmetrization. In the bosonic limit, however, the N = 2 system of equations lead to a new coupled integrable system of equations. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

δ/γ transformation in non-equilibrium solidified peritectic Fe-Ni alloy

Through phase transformation kinetic analysis and experimental observation, the δ/γ transformation occurring in the non-equilibrium peritectic Fe-4.33at.%Ni alloys was systematically investigated. According to JMA solid-state transformation kinetic theory, the Time-Temperature-Transformation (TTT) curves of the δ/γ transformation in peritectic Fe-Ni alloy were calculated. On this basis, the physical correlation between the δ/γ transformation and the initial undercooling of melt (△T) was elucidated. The results indicate that the change of △T can alter not only the overall δ/γ transformation pathways but also the transformation fraction with respect to each transformation mechanism.     

<Emphasis Type="Italic">Q</Emphasis> kink of the nonlinear <Emphasis Type="Italic">O</Emphasis>(3) <Emphasis Type="Italic">σ</Emphasis> model involving an explicitly broken symmetry

The (1 + 1)-dimensional nonlinear O(3) σ model involving an explicitly broken symmetry is considered. Sphalerons are known to exist in this model. These sphalerons are of a topological origin and are embedded kinks of the sine-Gordon model. In the case of a compact spatial manifold S ¹, sine-Gordon multikinks exist in the model. It is shown that the model admits a nonstatic generalization of the sine-Gordon kink/multikink, Q kink/multikink. Explicit expressions are obtained for the dependence of the Q kink energy and charge on the phase frequency of rotation. The Q kink is studied for stability, and expressions are obtained for the eigenfunctions and eigenfrequencies of the operator of quadratic fluctuations. It is shown that the Q kink is unstable over the entire admissible frequency range ω ∈ [−1, 1]. The one-loop quantum correction to the static-kink mass is calculated, and the Q-kink zero mode is quantized. It is shown that, in a general static case, the field equations of the model are integrable in quadratures.