Superconformal structures on the three-sphere

With the motivation to develop superconformal field theory on S^3, we introduce a 2n-extended supersphere S^{3|4n}, with n=1,2,..., as a homogeneous space of the three-dimensional Euclidean superconformal group OSp(2n|2,2) such that its bosonic body is S^3. Supertwistor and bi-supertwistor realizations of S^{3|4n} are derived. We study in detail the n=1 case, which is unique in the sense that the R-symmetry subgroup SO^*(2n) of the superconformal group is compact only for n=1. In particular, we show that the OSp(2|2,2) transformations preserve the chiral subspace of S^{3|4}. Several supercoset realizations of S^{3|4n} are presented. Harmonic/projective extensions of the supersphere by auxiliary bosonic fibre directions are sketched.Comment: 44 pages; V2: references added, typos corrected; V3: comments in Appendix B correcte

Dust particle formation in silane plasmas

Dust can be found anywhere: in the kitchen, in the car, in space… Not surprisingly we also see dust in commercial and laboratory plasmas. Dust can be introduced in the plasma, but it can also grow there by itself. In the microelectronics industry, contamination of the processing plasma by dust is an unacceptable phenomenon. People have put a lot of effort fighting the dust formation in plasmas. However, recent discoveries have proven that particles can also be used in the production of more efficient and stable solar cells and in single electron microelectronics devices. Particles that are used there have crystalline structure and a typical size of several nanometres. Since visible light has a wavelength of more than 400 nanometres, these particles cannot be detected optically; hence, new diagnostics are needed. In most cases, the active gas used in the discharges is silane – SiH4. This work is devoted to the study of the particle formation in silane containing plasmas. The commonly accepted mechanism of dust formation in a low-pressure silane plasma consists of several stages. First, silane radicals produce crystallite clusters of several nanometres in diameter. These clusters, when they reach a critical concentration, approximately equal to the concentration of ions in the plasma, start to agglomerate to form particles of 20 – 50 nm. These bigger dust formations no longer possess the crystallite structure of the initial clusters. All further growth is happening on the surface of the agglomerates. In the first part of this thesis we show that by following the behaviour of the fourth harmonic of the rf current enables us to identify phases of the particle formation. As a result we obtain a temperature dependence of the agglomeration time, which is the time before the nano-crystallites start to agglomerate. In agreement with previous observations, we show that a higher gas temperature slows down the particle formation process. In our experiments we have obtained an exponential dependence of the agglomeration time on temperature, which has not been reported before. Next, the agglomeration time dependence on the gas flow is studied. We present a semi-empirical particle formation model, explaining both flow and temperature dependence of the agglomeration time. Depending on the experimental conditions, several possible scenarios of the flow dependence have been proposed, many of which are also demonstrated to exist in the experimental results. We also point out the issue of the extra silane consumption from the vacuum volume, which strongly affects the speed of the particle formation and has not been addressed before. Then we give a general theory of the photodetachment experiment already developed before, with, however, a not yet addressed problem of the applicability. We use a small dielectric probe inside a microwave cavity to create a relatively big local perturbation of the medium inside the cavity. We then apply the principles of the microwave resonance technique to this situation and compare the calculated response of the cavity with the experimental values. Results of this test allow us to conclude that the medium perturbations caused by the extra electrons created during the photodetachment are small enough not to affect the results of the discussed theory for Summary 88 the laser induced photodetachment combined with the microwave resonance measurement technique. A new set-up has been built applying the microwave resonance technique to the fast measurements of the average electron density during the particle formation. The obtained results reveal several features that have not been observed before. The electron density in a silane containing discharge experiences a peak at around 300 µs after the discharge ignition. The electron density peak value in the silane/helium/argon mixture is higher that that in pure argon, which can easily be explained by a lower ionisation potential of silane compared to the ones of helium and of argon. However, the electronegativity of silane radicals quickly results in a decrease of the electron density, which results in the fact that, already 2 ms after the plasma ignition, the electron density in silane mixture is lower than in a pure argon discharge at the same rf power. In parallel with the electron density measurements we have also performed electrical measurements of the electrode self-bias and the rf harmonic amplitudes. We show, that during the first milliseconds of the discharge a noticeable decrease of the electron density (about 60 %) does not result in a significant change of the measured third harmonic of the rf current amplitude and the rf electrode self-bias voltage. We also study the electron density evolution during the particle agglomeration. As was already measured before, the particle agglomeration results in a drop of the electron density up to one order of magnitude. The change in the electrical parameters, however, is less drastic, although it is still possible to correlate the moment of the onset of the agglomeration with the evolution of the harmonic amplitudes of the rf current. At 1200C gas temperature we also looked at the evolution of the electron density for the first twenty-five milliseconds after the discharge ignition. We show that at 1200C the electron density drops about two times faster than in the experiments at 200C, indicating a higher electron loss rate at higher gas temperatures. Finally, we also briefly discuss the issue of plasma bursts, a phenomenon when the plasma suddenly spreads out of the discharge chamber, switching to another regime of operation, which results in a major increase in the electrode self-bias voltage, but not in the average electron density in the discharge chamber

String Amplitudes and Frame-like Formalism for Higher Spins

We analyze open string vertex operators describing connection gauge fields for spin 3 in Vasiliev's frame-like formalism and perform their extended BRST analysis. Gauge symmetry transformations, generalized zero torsion constraints relating extra fields to the dynamical frame-like field and relation between dynamical frame-like field and fully symmetric Fronsdal's field for spin 3 are all realized in terms of BRST constraints on these vertex operators in string theory. Using the construction, we analyze the 3-point correlator for spin 3 field and calculate Chern-Simons type cubic interactions described by 3-derivative Berends-Burgers-van Dam (BBD) type vertex in the frame-like formalism.Comment: 25 page

Cauchy Biorthogonal Polynomials

The paper investigates the properties of certain biorthogonal polynomials appearing in a specific simultaneous Hermite-Pade' approximation scheme. Associated to any totally positive kernel and a pair of positive measures on the positive axis we define biorthogonal polynomials and prove that their zeroes are simple and positive. We then specialize the kernel to the Cauchy kernel 1/{x+y} and show that the ensuing biorthogonal polynomials solve a four-term recurrence relation, have relevant Christoffel-Darboux generalized formulae, and their zeroes are interlaced. In addition, these polynomial solve a combination of Hermite-Pade' approximation problems to a Nikishin system of order 2. The motivation arises from two distant areas; on one side, in the study of the inverse spectral problem for the peakon solution of the Degasperis-Procesi equation; on the other side, from a random matrix model involving two positive definite random Hermitian matrices. Finally, we show how to characterize these polynomials in term of a Riemann-Hilbert problem.Comment: 38 pages, partially replaces arXiv:0711.408

Multiple ionization of neon by soft X-rays at ultrahigh intensity

At the free-electron laser FLASH, multiple ionization of neon atoms was quantitatively investigated at 93.0 eV and 90.5 eV photon energy. For ion charge states up to 6+, we compare the respective absolute photoionization yields with results from a minimal model and an elaborate description. Both approaches are based on rate equations and take into acccout a Gaussian spatial intensity distribution of the laser beam. From the comparison we conclude, that photoionization up to a charge of 5+ can be described by the minimal model. For higher charges, the experimental ionization yields systematically exceed the elaborate rate based prediction.Comment: 10 pages, 3 figure

The degenerate gravitino scenario

In this work, we explore the "degenerate gravitino" scenario where the mass difference between the gravitino and the lightest MSSM particle is much smaller than the gravitino mass itself. In this case, the energy released in the decay of the next to lightest sypersymmetric particle (NLSP) is reduced. Consequently the cosmological and astrophysical constraints on the gravitino abundance, and hence on the reheating temperature, become softer than in the usual case. On the other hand, such small mass splittings generically imply a much longer lifetime for the NLSP. We find that, in the constrained MSSM (CMSSM), for neutralino LSP or NLSP, reheating temperatures compatible with thermal leptogenesis are reached for small splittings of order 10^{-2} GeV. While for stau NLSP, temperatures of 4x10^9 GeV can be obtained even for splittings of order of tens of GeVs. This "degenerate gravitino" scenario offers a possible way out to the gravitino problem for thermal leptogenesis in supersymmetric theories.Comment: 27 pages, 10 figures and 1 table. Minor typos and references fixed. Matches published version in JCAP