N=2 Supermultiplet of Currents and Anomalous Transformations in Supersymmetric Gauge Theory

We examine some properties of supermultiplet consisting of the U(1)_{J} current, extended supercurrents, energy-momentum tensor and the central charge in N=2 supersymmetric Yang-Mills theory. The superconformal improvement requires adding another supermultiplet beginning with the U(1)_{R} current. We determine the anomalous (quantum mechanical) supersymmetry transformation associated with the central charge and the energy-momentum tensor to one-loop order.Comment: 8 pages, LaTe

Vertex Operators and Soliton Time Delays in Affine Toda Field Theory

In a space-time of two dimensions the overall effect of the collision of two solitons is a time delay (or advance) of their final trajectories relative to their initial trajectories. For the solitons of affine Toda field theories, the space-time displacement of the trajectories is proportional to the logarithm of a number $X$ depending only on the species of the colliding solitons and their rapidity difference. $X$ is the factor arising in the normal ordering of the product of the two vertex operators associated with the solitons. $X$ is shown to take real values between $0$ and $1$. This means that, whenever the solitons are distinguishable, so that transmission rather than reflection is the only possible interpretation of the classical scattering process, the time delay is negative and so an indication of attractive forces between the solitons.Comment: p. 24 Latex, Swansea-SWAT/93-94/3

Orthogonal Decomposition of Some Affine Lie Algebras in Terms of their Heisenberg Subalgebras

In the present note we suggest an affinization of a theorem by Kostrikin et.al. about the decomposition of some complex simple Lie algebras ${\cal G}$ into the algebraic sum of pairwise orthogonal Cartan subalgebras. We point out that the untwisted affine Kac-Moody algebras of types $A_{p^m-1}$ ($p$ prime, $m\geq 1$), $B_r, \, C_{2^m}, D_r,\, G_2,\, E_7,\, E_8$ can be decomposed into the algebraic sum of pairwise or\-tho\-go\-nal Heisenberg subalgebras. The $A_{p^m-1}$ and $G_2$ cases are discussed in great detail. Some possible applications of such decompositions are also discussed.Comment: 16 pages, LaTeX, no figure

Little Groups of Preon Branes

Little groups for preon branes (i.e. configurations of branes with maximal (n-1)/n fraction of survived supersymmetry) for dimensions d=2,3,...,11 are calculated for all massless, and partially for massive orbits. For massless orbits little groups are semidirect product of d-2 translational group $T_{d-2}$ on a subgroup of (SO(d-2) $\times$ R-invariance) group. E.g. at d=9 the subgroup is exceptional $G_2$ group. It is also argued, that 11d Majorana spinor invariants, which distinguish orbits, are actually invariant under d=2+10 Lorentz group. Possible applications of these results include construction of field theories in generalized space-times with brane charges coordinates, different problems of group's representations decompositions, spin-statistics issues.Comment: LaTeX, 11 page

Helicity, polarization, and Riemann-Silberstein vortices

Riemann-Silberstein (RS) vortices have been defined as surfaces in spacetime where the complex form of a free electromagnetic field given by F=E+iB is null (F.F=0), and they can indeed be interpreted as the collective history swept out by moving vortex lines of the field. Formally, the nullity condition is similar to the definition of "C-lines" associated with a monochromatic electric or magnetic field, which are curves in space where the polarization ellipses degenerate to circles. However, it was noted that RS vortices of monochromatic fields generally oscillate at optical frequencies and are therefore unobservable while electric and magnetic C-lines are steady. Here I show that under the additional assumption of having definite helicity, RS vortices are not only steady but they coincide with both sets of C-lines, electric and magnetic. The two concepts therefore become one for waves of definite frequency and helicity. Since the definition of RS vortices is relativistically invariant while that of C-lines is not, it may be useful to regard the vortices as a wideband generalization of C-lines for waves of definite helicity.Comment: 5 pages, no figures. Submitted to J of Optics A, special issue on Singular Optics; minor changes from v.

Poincar\'e recurrence theorem and the strong CP-problem

The existence in the physical QCD vacuum of nonzero gluon condensates, such as $$, requires dominance of gluon fields with finite mean action density. This naturally allows any real number value for the unit ``topological charge'' $q$ characterising the fields approximating the gluon configurations which should dominate the QCD partition function. If $q$ is an irrational number then the critical values of the $\theta$ parameter for which CP is spontaneously broken are dense in $\mathbb{R}$, which provides for a mechanism of resolving the strong CP problem simultaneously with a correct implementation of $U_{\rm A}(1)$ symmetry. We present an explicit realisation of this mechanism within a QCD motivated domain model. Some model independent arguments are given that suggest the relevance of this mechanism also to genuine QCD.Comment: 8 pages, RevTeX, 3 figures. Revised after referee suggestions. Now includes model independent argument

Interpreting the High Frequency QPO Power Spectra of Accreting Black Holes

In the context of a relativistic hot spot model, we investigate different physical mechanisms to explain the behavior of quasi-periodic oscillations (QPOs) from accreting black holes. The locations and amplitudes of the QPO peaks are determined by the ray-tracing calculations presented in Schnittman & Bertschinger (2004a): the black hole mass and angular momentum give the geodesic coordinate frequencies, while the disk inclination and the hot spot size, shape, and overbrightness give the amplitudes of the different peaks. In this paper additional features are added to the existing model to explain the broadening of the QPO peaks as well as the damping of higher frequency harmonics in the power spectrum. We present a number of analytic results that closely agree with more detailed numerical calculations. Four primary pieces are developed: the addition of multiple hot spots with random phases, a finite width in the distribution of geodesic orbits, Poisson sampling of the detected photons, and the scattering of photons from the hot spot through a corona of hot electrons around the black hole. Finally, the complete model is used to fit the observed power spectra of both type A and type B QPOs seen in XTE J1550-564, giving confidence limits on each of the model parameters.Comment: 30 pages, 5 figures, submitted to Ap

Can the plasma PD-1 levels predict the presence and efficiency of tumor-infiltrating lymphocytes in patients with metastatic melanoma?

Background: The immune response in melanoma patients is locally affected by presence of tumor-infiltrating lymphocytes (TILs), generally divided into brisk, nonbrisk, and absent. Several studies have shown that a greater presence of TILs, especially brisk, in primary melanoma is associated with a better prognosis and higher survival rate. Patients and Methods: We investigated by enzyme-linked immunosorbent assay (ELISA) the correlation between PD-1 levels in plasma and the presence/absence of TILs in 28 patients with metastatic melanoma. Results: Low plasma PD-1 levels were correlated with brisk TILs in primary melanoma, whereas intermediate values correlated with the nonbrisk TILs, and high PD-1 levels with absent TILs. Although the low number of samples did not allow us to obtain a statistically significant correlation between the plasma PD-1 levels and the patients' overall survival depending on the absence/presence of TILs, the median survival of patients having brisk type TILs was 5 months higher than that of patients with absent and nonbrisk TILs. Conclusions: This work highlights the ability of measuring the plasma PD-1 levels in order to predict the prognosis of patients with untreated metastatic melanoma without a BRAF mutation at the time of diagnosis

Dark Energy and Dark Matter

It is a puzzle why the densities of dark matter and dark energy are nearly equal today when they scale so differently during the expansion of the universe. This conundrum may be solved if there is a coupling between the two dark sectors. In this paper we assume that dark matter is made of cold relics with masses depending exponentially on the scalar field associated to dark energy. Since the dynamics of the system is dominated by an attractor solution, the dark matter particle mass is forced to change with time as to ensure that the ratio between the energy densities of dark matter and dark energy become a constant at late times and one readily realizes that the present-day dark matter abundance is not very sensitive to its value when dark matter particles decouple from the thermal bath. We show that the dependence of the present abundance of cold dark matter on the parameters of the model differs drastically from the familiar results where no connection between dark energy and dark matter is present. In particular, we analyze the case in which the cold dark matter particle is the lightest supersymmetric particle.Comment: 4 pages latex, 2 figure