Conformal Blocks for admissible representations in SL(2) current algebra

We show how to deal with screening charges involving fractional powers of free fields. This enables us to use the free field Wakimoto construction to obtain complete expressions for integral representations of conformal blocks for N-point functions on the sphere, also in the case of non-integrable representations, in particular for admissible representations. We verify several formal properties including the Knizhnik-Zamolodchikov equations. We discuss the fusion rules which result from our treatment, and compare with the literature.Comment: 30 pages, LaTe

Free field realization of SL(2) correlators for admissible representations, and hamiltonian reduction for correlators

Talk presented by J.L. Petersen at the 29th Symposium Ahrenshop, Buckow August 29-September 2, 1995. A presentation is given of the free field realization relevant to SL(2) WZW theories with a Hilbert space based on admissible representations. It is known that this implies the presence of two screening charges, one involving a fractional power of a free field. We develop the use of fractional calculus for treating in general such cases. We derive explicit integral representations of $N$-point conformal blocks. We show that they satisfy the Knizhnik-Zamolodchikov equations and we prove how they are related to minimal conformal blocks via a formulation of hamiltonian reduction advocated by Furlan, Ganchev, Paunov and Petkova.Comment: 8 pages, LaTeX, article.sty, espcrc2.st

Some chiral rings of N=2 discrete superconformal series induced by SL(2) degenerate conformal field theories

By generalizing a fermionic construction, a natural relation is found between SL(2) degenerate conformal field theories and some N=2 discrete superconformal series. These non-unitary models contain, as a subclass, N=2 minimal models. The construction permits one to investigate the properties of chiral operators in the N=2 models. A chiral ring reveals a close connection with underlying quantum group structures.Comment: 19 pages, 2 figures, latex2

DEVELOPMENT OF PSYCHOPHYSICAL QUALITIES TO PROFESSIONAL ACTIVITY AT STUDENTS MEANS OF PHYSICAL TRAINING

The system of the organizational and pedagogical conditions provid-ing efficiency of formation of psychophysical readiness of students of high-er education institutions of a technical profile for professional activity with means of physical training is presented in article. The efficiency of the de-veloped program for formation of psychophysical readiness of future ex-perts for professional activity is noted. Need of essential improvement of system of professional and applied physical training for higher education institutions as vocational training of graduates lags behind qualifying standards modern life and modern working conditions is stated. Question-ing, sociological methods of researches, a pedagogical experiment are de-scribed; which were carried out on the basis of SEO НЕ "Donbass State Technical University", Alchevsk, LPR. For achievement of objectives of article social survey, both specialists graduates, and students of this higher education institution, was conducted by a problem of this poll, was to reveal working conditions, motivation degree to occupations physical training with use of applied exercises. As a basis for carrying out an ex-periment pedagogical approaches which are directed to specialization of process of physical training in a higher educational institution were usedВ статье представлена система организационно-педагогических условий, обеспечивающих эффективность формирования психофизической готовности студентов вузов технического профиля к профессиональной деятельности средствами физического воспитания. Отмечена эффективность разработанной программы по формированию психофизической готовности будущих специалистов к профессиональной деятельности. Излагается необходимость существенного совершенствования системы профессионально-прикладной физической подготовки в вузах, так как профессиональная подготовка выпускников отстает от предъявляемых требований современной жизнью и современными условиями труда. Описываются анкетирование, социологические методы исследований, педа-гогический эксперимент; которые проводились на базе ГОО ВПО «Донбасский государственный технический университет», г. Алчевск, ЛНР. Для достижения поставленных задач статьи был проведен социальный опрос, как специалистов-выпускников, так и студентов данного ВУЗа, задачей данного опроса, было выявить условия труда, степень мотивации к занятиям физическим воспитанием с использованием прикладных упражнений. В качестве основы для про-ведения эксперимента были использованы педагогические подходы, которые направлены на специализацию процесса физического воспитания в высшем учебном заведени

An Infinite Number of Commuting Quantum W^∞\hat{W}_{\infty} Charges in the SL(2,R)/U(1)SL(2,R)/U(1) Coset Model

The conformal non-compact $SL(2,R)/U(1)$ coset model in two dimensions has been recently shown to embody a nonlinear $\hat{W}_\infty$ current algebra, consisting of currents of spin $\geq 2$ including the energy-momentum tensor. In this letter we explicitly construct an infinite set of commuting quantum $\hat{W}_\infty$ charges in the model with $k=1$. These commuting quantum charges generate a set of infinitely many compatible flows (quantum KP flows), which maintain the nonlinear $\hat{W}_\infty$ current algebra invariant.Comment: 15

Fusion, Crossing and Monodromy in Conformal Field Theory Based on SL(2)SL(2) Current Algebra with Fractional Level

Based on our earlier work on free field realizations of conformal blocks for conformal field theories with $SL(2)$ current algebra and with fractional level and spins, we discuss in some detail the fusion rules which arise. By a careful analysis of the 4-point functions, we find that both the fusion rules previously found in the literature are realized in our formulation. Since this is somewhat contrary to our expectations in our first work based on 3-point functions, we reanalyse the 3-point functions and come to the same conclusion. We compare our results on 4-point conformal blocks in particular with a different realization of these found by O. Andreev, and we argue for the equivalence. We describe in detail how integration contours have to be chosen to obtain convenient bases for conformal blocks, both in his and in our own formulation. We then carry out the rather lengthy calculation to obtain the crossing matrix between s- and t-channel blocks, and we use that to determine the monodromy invariant 4-point greens functions. We use the monodromy coefficients to obtain the operator algebra coefficients for theories based on admissible representations.Comment: 42 Pages, LaTeX, uses pictex.sty, alternatively prepictex.tex, pictex.tex, postpictex.te

Perturbation expansion for the diluted two-dimensional XY model

We study the quasi-long-range ordered phase of a 2D XY model with quenched site-dilution using the spin-wave approximation and expansion in the parameter which characterizes the deviation from completely homogeneous dilution. The results, obtained by keeping the terms up to the third order in the expansion, show good accordance with Monte Carlo data in a wide range of dilution concentrations far enough from the percolation threshold. We discuss different types of expansion.Comment: 8 pages, 1 eps figure, style file include

Polymers and percolation in two dimensions and twisted N=2 supersymmetry

It is shown how twisted N=2 (k=1) provides for the first time a complete conformal field theory description of the usual geometrical phase transitions in two dimensions, like polymers, percolation or brownian motion. In particular, four point functions of operators with half integer Kac labels are computed, together with geometrical operator products. In addition to Ramond and Neveu Schwartz, a sector with quarter twists has to be introduced. The role of fermions and their various sectors is geometrically interpreted, modular invariant partition functions are built. The presence of twisted N=2 is traced back to the Parisi Sourlas supersymmetry. It is shown that N=2 leads also to new non trivial predictions; for instance the fractal dimension of the percolation backbone in two dimensions is conjectured to be D=25/16, in good agreement with numerical studies.Comment: 42 pages (without figures

Magnetocrystalline anisotropy of the multiphase samples of the hexaferrites Ba2Ni2-xCuxFe12O22 studied by the ferromagnetic resonance method

This paper presents structural and magnetic investigation of the hexaferrites Ba2Ni2-xCuxFe12O22 system in the Cu2+ concentration range 0 ≤ x ≤ 1.4. Samples were synthesized according to traditional ceramic processing technology. The samples were multiphase, since the optimal conditions of synthesis were not specially worked out. According to the data of X-ray diffraction analysis, the samples contain both a target phase and impurity phases of magnetite and hematite, as well as hexagonal phase of Ba-M. The values of the saturation magnetization of the samples were a little more than the values in the literature. It could be explained by the contribution from impurity phases with large magnetization values. The values of the anisotropy fields of the separate phases, which are contained in the investigated samples, were determined by the method of ferromagnetic resonance. The anisotropy field decreases with an increase in the content of copper ion. It is show that the value of the anisotropy field of hexaferrite Ni2Y is close to the literature value