The spinning superparticle

Doubly graded massless supersymmetric particle models with both world-line local and space-time global supersymmetry are considered. We describe the first quantization of the model with four-dimensional space-time and N=1 world-line SUSY. Using the Gupta-Bleuler method we obtain as the super wave-function a pair of D=4 chiral spinor superfields with the on-shell spectrum containing scalar and vector multiplets.     

Conformal supergravity in ten dimensions

We present the complete off-shell structure of conformal supergravity in ten dimensions. It is based on 128 + 128 degrees of freedom and its formulation requires differential constraints. We study how these constraints are resolved in four and five dimensions. Covariant conditions are given that restrict conformal supergravity to its on-shell Poincaré counterpart. In ten dimensions the relationship between the two theories has new and unusual aspects, which we explore in a variety of ways. We rewrite on-shell Poincaré supergravity in a superconformally invariant form, from which we deduce that its off-shell version must contain at least a scalar (chiral) multiplet. We analyze some aspects of the non-linear structure of the field representation based on the conformal fields combined with one scalar multiplet.     

On superspace supergravity in ten dimensions

Off-shell N=1, d=10 supergravity splits into a (128+128)-component multiplet and two scalar superfields. A concise formulation of the superspace contraints corresponding to the (128+128)-multiplet is given and the incorporation of the dimension - 6 scalar superfield discussed at the linearized level. The second scalar superfield, whose leading component is the physical dilaton field, may be regarded as being external to the superspace geometry. An action for the full non-linear theory is proposed.     

Stable spinning optical solitons in three dimensions

We introduce spatiotemporal spinning solitons (vortex tori) of the three-dimensional nonlinear Schr?dinger equation with focusing cubic and defocusing quintic nonlinearities. The first ever found completely stable spatiotemporal vortex solitons are demonstrated. A general conclusion is that stable spinning solitons are possible as a result of competition between focusing and defocusing nonlinearities.     

Mean-field gauge interactions in five dimensions II. The orbifold

We study Gauge–Higgs Unification in five dimensions on the lattice by means of the mean-field expansion. We formulate it for the case of an SU(2)$\mathit{SU}(2)$ pure gauge theory and orbifold boundary conditions along the extra dimension, which explicitly break the gauge symmetry to U(1)$U(1)$ on the boundaries. Our main result is that the gauge boson mass computed from the static potential along four-dimensional hyperplanes is non-zero implying spontaneous symmetry breaking. This observation supports earlier data from Monte Carlo simulations in Irges and Knechtli (2007) [12].     

The super-Poincaré algebra and the scalar superfield in ten dimensions

The super-Poincaré algebra in 10 dimensions is examined. The differences with respect to the other cases are pointed out. In particular, the scalar superfield is considered in detail as an example.     

Anomaly-free supergravity and super-Yang-Mills theories in ten dimensions

We formulate in ten dimensions a supergravity theory coupled to a super-Yang-Mills theory through the Green-Schwarz ansatz, which ensures chiral anomaly cancellation. The formulation is obtained by fixing suitable constraints in the superspace and solving the Bianchi identities. In this way we obtain the whole set of equations of motion. They are characterized by highly non-polynomial expressions, when expressed only in terms of the physical superfields. We discuss the problem of the massive modes appearing in some of these equations.     

The Yukawa coupling of quantum fields in two dimensions. II

The Yukawa coupling in two dimensional space time is considered. A space outoff is introduced in the interaction termV, so that the renormalized HamiltonianH _ren is a rigorously defined bilinear form in the Fock Hilbert space. The main result is thatH _ren is positive provided the finite part of the renormalization terms are suitably chosen. As a consequence, the Schrödinger equation (i/t–H _ren)=0 can be solved.This work was supported in part by the National Science Foundation, GP — 6165.     

The standard model from a gauge theory in ten dimensions via CSDR

We present a gauge theory in ten dimensions based on the gauge group E₈ which is dimensionally reduced, according to the coset space dimensional reduction (CSDR) scheme, to the standard model SU_3c×SU_2L×U₁, which breaks further to SU_3c×U_1em. We use the coset space Sp₄/(SU₂×U₁)×Z₂. The model gives similar predictions for sin²θ_w and proton decay as the minimal SU₅ GUT. Natural choices of parameters suggest that the Higgs masses are as predicted by the Coleman-Weinberg radiative mechanism.     

The Ne II spectrum

Spectra of neon-filled hollow cathode discharge lamps were observed by means of high-resolution Fourier-transform spectroscopy (FTS) covering the region from vacuum ultraviolet to near infrared. By combining these new measurements with results of other FTS and grating spectroscopy observations, we compiled a complete list of approximately 1700 spectral lines of Ne II covering the range from 324 ? to 130000 ?. All known energy levels of Ne II were derived from this line list with improved accuracy. The newly optimized energy levels were used to derive a set of Ritz wavelength standards in the vacuum ultraviolet that are in good agreement with the previously used data. An improved classification of energy levels was made with the help of parametric calculations, and the existing controversy in the naming of strongly mixed levels was resolved. Electronic supplementary material Online Material     

Massive N = 2a supergravity in ten dimensions

A new version of the non-chiral N = 2a supergravity in ten dimensions is obtained, in which the two-index tensor field of the theory “eats” the single vector field and acquires a mass in a Higgs-type mechanism. The new theory, although it contains no fundamental vectors, bears many formal resemblances to gauged supergravities (in particular, the recently constructed F(4) theory in six dimensions). The scalar potential has no extrema, but nevertheless the classical equations of motion admit a wide variety of spontaneous compactifications, many to four dimensions.     

A low-lying resonance in the spectrum of H II. The 2P state

The wave function containing 20 parameters and the corresponding energy of the 2¹P state of H^- were calculated. As is well known this state lies in the H^- continuum. The inclusion of this state in the expansion of the continuum wave function can drastically influence the cross-section of an electron scattered by a hydrogen atom in the energy region involved. This bound pseudo-state will, in any case, influence the continuum absorption coefficient, but it may be insufficient to guarantee a peak in this absorption coefficient or in any e^-H experiment. Anyway, a new 2¹P virtual state of H^- is obtained with an energy of approximately -0.92 Ry. The exact position of the resonance needed to account for the occurrence of the interstellar line at 6180 Å is -0.9079 Ry. Since this resonance must lie very near the position of the bound state, our results support the identification of the broad feature at 6180 Å as a transition in H^-.     

A stochastic approach to the hadron spectrum. II

The definition of mass as a random variable is applied to the study of the decay rates. A decay is assumed possible when the fluctuation of the Gaussian variables involved makes a definite relation satisfied. Computing the probability of this process leads to the determination of the decay amplitude. This calculation, unified for baryons and mesons, is worked out in the lower and medium spectrum (up to2000 MeV for baryons and mesons), and fits to20 MeV the accurate measurements of width and branching ratios.     

Constructing unified models based on E8 in ten dimensions

The vacuum energy is calculated for Yang-Mills (YM) system defined inD dimensional space-time ofS ¹×R ^d (D=d+1), where the possibility of the YM fields to acquire the vacuum expectation values onS ¹ is taken into account. The vacuum energy has already been obtained to the order of one-loop in many people. Here we calculate the vacuum energy inD dimensions to two-loop order. With an intention to reach higher loops, an approximation method is proposed, which is especially effective in higher dimensions. By this method, we can treat the higher-loop contributions of YM interactions as easily as we treat one-loop effect. As a check, we show reproduction of the two-loop contribution (D-dependence of the coefficient as well as the functional form) when the coupling constant is small. This approximation method is useful not only for the Kaluza-Klein theories but also for the finite temperature-density system (as a quark-gluon plasma).Minami-Ohsawa Hachioji-shi, Tokyo 92-03 Japan     

Intersections of random walks in four dimensions. II

Letf(n) be the probability that the paths of two simple random walks of lengthn starting at the origin in ⁴ have no intersection. It has previously been shown thatf(n)c(logn)^–1/2. Here it is proved that for allr>1/2, .Research Supported by NSF grant MCS-8301037