<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.     

<Emphasis Type="Italic">SU</Emphasis>(5) symmetry of<Emphasis Type="Italic">spdfg</Emphasis> interacting boson model

The extended interacting boson model withs-, p-, d-, f- andg-bosons included (spdfg IBM) is investigated. The algebraic structure including the generators, the Casimir operators of the groups at theSU(5) dynamical symmetry and the branching rules of the irreducible representation reductions along the group chain are obtained. The typical energy spectrum of the symmetry is given.     

<Emphasis Type="Italic">SU</Emphasis><Subscript><Emphasis Type="Italic">L</Emphasis></Subscript>(4)×<Emphasis Type="Italic">U</Emphasis>(1) model for electroweak unification and sterile neutrinos

Some of the basic problems in neutrino physics, such as new energy scales, the enormous gap between the neutrino masses and the lightest charged fermion mass, and the possible existence of sterile neutrinos in the eV mass range are studied in the local gauge group SU _L (4)×U(1) for electroweak unification, which does not contain fermions with exotic electric charges. It is shown that the neutrino mass spectrum can be decoupled from that of the other fermions. The further normal seesaw mechanism for neutrinos, with right-handed neutrino Majorana masses of order M≫M _weak as well a new eV-scale can be accommodated. The eV-scale seesaw may manifest itself in experiments like the Liquid Scintillation Neutrino Detector (LSND) and MiniBooNE (MB) experimental results and future neutrino experiments.     

A reanalysis of finite temperature <Emphasis Type="Italic">SU</Emphasis>(<Emphasis Type="Italic">N</Emphasis>) gauge theory

We revise the SU(N _c ), N _c =3,4,6, lattice data on pure gauge theories at finite temperature by means of a quasi-particle approach. In particular, we focus on the relation between the effective mass of the quasi-particle and the order of the deconfinement transition, the scaling of the interaction measure with N²_c -1N^{2}_{c} -1, the role of gluon condensate, and the screening mass.     

Trace anomaly and quasi-particles in finite temperature <Emphasis Type="Italic">SU</Emphasis>(<Emphasis Type="Italic">N</Emphasis>) gauge theory

We consider deconfined matter in SU(N) gauge theory as an ideal gas of transversely polarized quasi-particle modes having a temperature-dependent mass m(T). Just above the transition temperature, the mass is assumed to be determined by the critical behavior of the energy density and the screening length in the medium. At high temperature, it becomes proportional to T as the only remaining scale. The resulting (trace anomaly based) interaction measure Δ=(ϵ−3P)/T ⁴ and energy density are found to agree well with finite temperature SU(3) lattice calculations.     

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.     

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.     

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.     

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.     

Conformal Continuations in Gravitation Theory with Lagrangian <Emphasis Type="Italic">F</Emphasis>(<Emphasis Type="Italic">R</Emphasis>)

Static spherically-symmetric vacuum solutions of gravitation theory equations with Lagrangian f(R) are examined, where R is a scalar curvature and f is an arbitrary function. Equations of f(R)-theories are reduced to the Einstein scenario — general relativity theory (GRT) equations with a source in the form of a scalar field with potential — with the use of the well-known conformal transformation. The necessary and sufficient conditions of existence of solutions admitting conformal continuations are formulated. This means that the central singularity of the Einstein scenario is mapped into a regular sphere S_trans of the Jordan scenario (that is, into the manifold corresponding to the initial formulation of the theory), and a solution of the field equations can be smoothly continued through it. The value of curvature R on the sphere S_trans corresponds to an extremum of the function f(R). Concrete examples are considered. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 46–51, September, 2005.     

<Emphasis Type="Italic">X</Emphasis>(3): An exactly separable <Emphasis Type="Italic">γ</Emphasis>-rigid version of the <Emphasis Type="Italic">X</Emphasis>(5) critical point symmetry

A γ-rigid version (with γ = 0) of the X(5) critical point symmetry is constructed. The model, to be called X(3) since it is proved to contain three degrees of freedom, utilizes an infinite well potential, is based on exact separation of variables, and leads to parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates which are in good agreement with existing experimental data for ¹⁷²Os and ¹⁸⁶Pt. An unexpected similarity of the β ₁ bands of the X(5) nuclei ¹⁵⁰Nd, ¹⁵²Sm, ¹⁵⁴Gd, and ¹⁵⁶Dy to the X(3) predictions is observed. The text was submitted by the authors in English.     

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.      

<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     

<Emphasis Type="Italic">SU</Emphasis>(2|1) supersymmetric mechanics as a deformation of <Emphasis Type="Italic">N</Emphasis> = 4 mechanics

We give a brief review of SU(2|1) supersymmetric quantum mechanics based on the worldline realizations of the supergroup SU(2|1) in the appropriate N = 4, d = 1 superspaces. The corresponding SU(2|1) models are deformations of standard N = 4, d = 1 models by a mass parameter m.     

Fusion Rules for the Vertex Operator Algebras <Emphasis Type="Italic">M</Emphasis>(1)<Superscript>+</Superscript> and <Emphasis Type="Italic">V</Emphasis><Superscript>+</Superscript><Subscript><Emphasis Type="Italic">L</Emphasis></Subscript>

The fusion rules for the vertex operator algebras M(1)⁺ (of any rank) and V⁺_L (for any positive definite even lattice L) are determined completely.Supported by JSPS Research Fellowships for Young ScientistsPartially supported by NSF grants and a research grant from the Committee on Research, UC Santa CruzPartially supported by a NSA grant and a grant from Rutgers University Research Council     

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.     

Singlet Deformation of <Emphasis Type="Italic">N</Emphasis> = (1,1) Superspace

We discuss the SO(4) × SU(2) invariant deformation of the Euclidean N = (1,1) supersymmetric theories in the framework of the harmonic superspace.     

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)     

<Emphasis Type="Italic">D</Emphasis>-Branes in the Euclidean <Emphasis Type="Italic">AdS</Emphasis><Subscript>3</Subscript> and <Emphasis Type="Italic">T</Emphasis>-Duality

We show that D-branes in the Euclidean AdS ₃ can be naturally associated to the maximally isotropic subgroups of the Lu–Weinstein double of SU(2). This picture makes very transparent the residual loop group symmetry of the D-brane configurations and gives also immediately the D-branes shapes and the σ-model boundary conditions in the de Sitter T-dual of the SL(2,C)/SU(2) WZW model.