BF Theories and Group-Level Duality

It is known that the partition function and correlators of the two-dimensional topological field theory $G_K(N)/ G_K(N)$ on the Riemann surface $\Sigma_{g,s}$ is given by Verlinde numbers, dim($V_{g,s,K}$) and that the large $K$ limit of dim($V_{g,s,K}$) gives Vol(${\cal M}_s$), the volume of the moduli space of flat connections of gauge group $G(N)$ on $\Sigma_{g,s}$, up to a power of $K$. Given this relationship, we complete the computation of Vol(${\cal M}_s$) using only algebraic results from conformal field theory. The group-level duality of $G(N)_K$ is used to show that if $G(N)$ is a classical group, then $\displaystyle \lim_{N\rightarrow \infty} G_K(N) / G_K(N)$ is a BF theory with gauge group $G(K)$. Therefore this limit computes Vol(${\cal M}^\prime_s$), the volume of the moduli space of flat connections of gauge group $G(K)$

Penrose Limits and Spacetime Singularities

We give a covariant characterisation of the Penrose plane wave limit: the plane wave profile matrix $A(u)$ is the restriction of the null geodesic deviation matrix (curvature tensor) of the original spacetime metric to the null geodesic, evaluated in a comoving frame. We also consider the Penrose limits of spacetime singularities and show that for a large class of black hole, cosmological and null singularities (of Szekeres-Iyer ``power-law type''), including those of the FRW and Schwarzschild metrics, the result is a singular homogeneous plane wave with profile $A(u)\sim u^{-2}$, the scale invariance of the latter reflecting the power-law behaviour of the singularities.Comment: 9 pages, LaTeX2e; v2: additional references and cosmetic correction

Fretting wear of Ti(CxNy) PVD coatings under variable environmental conditions

Fretting wear as a specific type of degradation is defined as an oscillatory motion at small amplitude between two nominally stationary solid bodies in mutual contact. Under external stresses the interface is being damaged by debris generation and its successive ejections outside the contact area. A potential protection against fretting damage by means of hard coatings is being offered by different surface engineering techniques. For this study TiC, TiN and TiCN hard coatings manufactured by a PVD method have been selected and tested against smooth polycrystalline alumina ball. A fretting test programme has been carried out at the frequency of 5Hz, 100N normal load, 100µm displacement amplitude and at three values of a relative humidity: 10, 50 and 90% at 295-298K temperature. It turned out that the intensity of wear process was depending not only on loading conditions but on environmental ones as well. A significant impact of RH on wear rate and friction behaviour of the coatings under investigation has been observed. Two different damage mechanisms have been identified and related to the phenomena of debris oxidation and debris adhesion to the counterbody surface. In the latter case the debris deposited onto the surface of the alumina ball lead to a change of stress distribution at the interface and as a result to accelerated wear. In this work experiments with variable relative humidity increasing from 10% to 90% within 1 a single fretting test have been completed. It follows from these experiments that there exists an intermediate value of the RH at which the friction coefficient changes rapidly. Finally a dissipated energy approach has been applied in the work in order to quantify and compare fretting wear rates of different hard coatings

Исследование процесса шлифования стальных кулачков инструментом из кубического нитрида бора без охлаждения

Экспериментальными исследованиями, имитирующими шлифование кулачков из закаленной легированной стали, установлено, что их обработка с минимальным нагревом обрабатываемой поверхности с охлаждением масляным туманом или без охлаждения возможна высокопористым кругом из кубического нитрида бора. Выявлено, что для минимизации термодинамической напряженности сухого шлифования целесообразно назначать режим обработки с максимальной возможной глубиной врезания круга и минимальной скоростью вращения детали.Експериментальними дослідженнями, які імітують шліфування кулачків із загартованої легованої сталі, встановлено, що їх обробка з мінімальним нагрівом оброблюваної поверхні з охолодженням масляним туманом або без охолодження можлива високопористим кругом з кубічного нітриду бору. Виявлено, що для мінімізації термодинамічної напруженості сухого шліфування доцільно призначати режим обробки з максимальною можливою глибиною врізання круга і мінімальною швидкістю обертання деталі.Experimental studies simulating grinding of Cams of hardened alloy steel, determined that their treatment with the lowest heating of the surface cooled oil mist or without cooling are possible by using highly porous grinding wheels from cubic boron nitride. Also identified that to minimize the thermodynamic tension dry sanding it is advisable to appoint a mode of processing with the maximum possible depth plunging grinding wheel and a minimum speed of rotation of the part

Penrose Limits of the Baryonic D5-brane

The Penrose limits of a D5-brane wrapped on the sphere of AdS_5 x S^5 and connected to the boundary by M fundamental strings, which is dual to the baryon vertex of the N=4 SU(M) super Yang-Mills theory, are investigated. It is shown that, for null geodesics that lead to the maximally supersymmetric Hpp-wave background, the resulting D5-brane is a 1/2-supersymmetric null brane. For an appropriate choice of radial geodesic, however, the limiting configuration is 1/4-supersymmetric and closely related to the Penrose limit of a flat space BIon.Comment: LaTeX, 1+18 pages, 1 figure; v2: obvious misquotation of the number of preserved supersymmetries correcte

Supersymmetry and homogeneity of M-theory backgrounds

We describe the construction of a Lie superalgebra associated to an arbitrary supersymmetric M-theory background, and discuss some examples. We prove that for backgrounds with more than 24 supercharges, the bosonic subalgebra acts locally transitively. In particular, we prove that backgrounds with more than 24 supersymmetries are necessarily (locally) homogeneous.Comment: 19 pages (Erroneous Section 6.3 removed from the paper.

Geometry of Schroedinger Space-Times II: Particle and Field Probes of the Causal Structure

We continue our study of the global properties of the z=2 Schroedinger space-time. In particular, we provide a codimension 2 isometric embedding which naturally gives rise to the previously introduced global coordinates. Furthermore, we study the causal structure by probing the space-time with point particles as well as with scalar fields. We show that, even though there is no global time function in the technical sense (Schroedinger space-time being non-distinguishing), the time coordinate of the global Schroedinger coordinate system is, in a precise way, the closest one can get to having such a time function. In spite of this and the corresponding strongly Galilean and almost pathological causal structure of this space-time, it is nevertheless possible to define a Hilbert space of normalisable scalar modes with a well-defined time-evolution. We also discuss how the Galilean causal structure is reflected and encoded in the scalar Wightman functions and the bulk-to-bulk propagator.Comment: 32 page

On solvable models of type IIB superstring in NS-NS and R-R plane wave backgrounds

We consider type IIB string in the two plane-wave backgrounds which may be interpreted as special limits of the AdS_3 x S^3 metric supported by either the NS-NS or R-R 3-form field. The NS-NS plane-wave string model is equivalent to a direct generalization of the Nappi-Witten model, with its spectrum being similar to that of strings in constant magnetic field. The R-R model can be solved in the light-cone gauge, where the Green-Schwarz action describes 4 massive and 4 massless copies of free bosons and fermions. We find the spectra of the two string models and study the asymptotic density of states. We also discuss a more general class of exactly solvable plane-wave models with reduced supersymmetry which is obtained by adding twists in two spatial 2-planes.Comment: 36 pages, harvmac. v2: discussion of equivalence of the supergravity parts of the spectra of the NS-NS and R-R models added in sect.5.3; v3: added remark on periodicity of the NS-NS spectrum; v4: minor correction in sect.6.

pp-waves in 11-dimensions with extra supersymmetry

The Killing spinor equations for pp-wave solutions of eleven dimensional supergravity are analysed and it is shown that there are solutions that preserve 18,20,22 and 24 supersymmetries, in addition to the generic solution preserving 16 supersymmetries and the Kowalski-Glikman solution preserving 32 supersymmetries.Comment: 13 pages. Reference added, typos corrected, new examples of 7-parameter case presente

Uniqueness of M-theory PP-Wave Background with Extra Supersymmetries

We examine Killing spinor equations of the general eleven-dimensional pp-wave backgrounds, which contain a scalar H(x^m,x^-) in the metric and a three-form \xi(x^m,x^-) in the flux. Considering non-harmonic extra Killing spinors, we show that if the backgrounds admit at least one extra Killing spinor in addition to the standard 16 Killing spinors, they can be reduced to the form with H=A_{mn}(x^-)x^mx^n and \xi(x^-) modulo coordinate transformations. We further examine the cases in which the extra Killing spinor is characterized by a set of Cartan matrices. The super-isometry algebras of the resulting backgrounds are also derived.Comment: 25 pages, LaTeX2e, comments added, version to appear in PR