Bootstrapping the O(N) Vector Models

We study the conformal bootstrap for 3D CFTs with O(N) global symmetry. We obtain rigorous upper bounds on the scaling dimensions of the first O(N) singlet and symmetric tensor operators appearing in the $phi_i times phi_j$ OPE, where $phi_i$ is a fundamental of O(N). Comparing these bounds to previous determinations of critical exponents in the O(N) vector models, we find strong numerical evidence that the O(N) vector models saturate the bootstrap constraints at all values of N. We also compute general lower bounds on the central charge, giving numerical predictions for the values realized in the O(N) vector models. We compare our predictions to previous computations in the 1/N expansion, finding precise agreement at large values of N.

Conformal Blocks in the Large D Limit

We derive conformal blocks in an inverse spacetime dimension expansion. In this large D limit, the blocks are naturally written in terms of a new combination of conformal cross-ratios. We comment on the implications for the conformal bootstrap at large D.

Spinning Conformal Blocks

For conformal field theories in arbitrary dimensions, we introduce a method to derive the conformal blocks corresponding to the exchange of a traceless symmetric tensor appearing in four point functions of operators with spin. Using the embedding space formalism, we show that one can express all such conformal blocks in terms of simple differential operators acting on the basic scalar conformal blocks. This method gives all conformal blocks for conformal field theories in three dimensions. We demonstrate how this formalism can be applied in a few simple examples.

Carving Out the Space of 4D CFTs

We introduce a new numerical algorithm based on semidefinite programming to efficiently compute bounds on operator dimensions, central charges, and OPE coefficients in 4D conformal and N=1 superconformal field theories. Using our algorithm, we dramatically improve previous bounds on a number of CFT quantities, particularly for theories with global symmetries. In the case of SO(4) or SU(2) symmetry, our bounds severely constrain models of conformal technicolor. In N=1 superconformal theories, we place strong bounds on dim(Phi*Phi), where Phi is a chiral operator. These bounds asymptote to the line dim(Phi*Phi) <= 2 dim(Phi) near dim(Phi) ~ 1, forbidding positive anomalous dimensions in this region. We also place novel upper and lower bounds on OPE coefficients of protected operators in the Phi x Phi OPE. Finally, we find examples of lower bounds on central charges and flavor current two-point functions that scale with the size of global symmetry representations. In the case of N=1 theories with an SU(N) flavor symmetry, our bounds on current two-point functions lie within an O(1) factor of the values realized in supersymmetric QCD in the conformal window.

Evolution of Cool Close Binaries - Approach to Contact

A set of 27 evolutionary models of cool close binaries was computed under the assumption that their evolution is influenced by the magnetized winds. Initial periods of 1.5, 2.0 and 2.5 d were considered. For each period three values of 1.3, 1.1 and 0.9 solar mass were taken as the initial masses of the more massive components. Here the results of the computations of the first evolutionary phase are presented, which starts from the initial conditions and ends when the more massive component reaches its critical Roche lobe. In all considered cases this phase lasts for several Gyr. For binaries with the higher total mass and/or longer initial periods this time is equal to, or longer than the main sequence life time of the more massive component. For the remaining binaries it amounts to a substantial fraction of this life time. From the statistical analysis of models, the predicted period distribution of detached binaries with periods shorter than 2 d was obtained and compared to the observed distribution from the ASAS data. An excellent agreement was obtained under the assumption that the period distribution in this range is determined solely by the mass and angular momentum loss due to the magnetized winds. This result indicates, in particular, that virtually all cool detached binaries with periods of a few tenths of a day, believed to be the immediate progenitors of W UMa-type stars, were formed from detached systems with periods around 2-3 d and that magnetic braking is the dominant formation mechanism of cool contact binaries. It operates on the time scale of several Gyr rendering them rather old, with age of 6-10 Gyr. The results of the present analysis will be used as input data to investigate the subsequent evolution of the binaries, through the mass exchange phase and contact or semi-detached configuration till the ultimate merging of the components.

Challenges for stellar pulsation and evolution theory

During the last few decades, great effort has been made towards understanding hydrodynamical processes which determine the structure and evolution of stars. Up to now, the most stringent constraints have been provided by helioseismology and stellar cluster studies. However, the contribution of asteroseismology becomes more and more important, giving us an opportunity to probe the interiors and atmospheres of very different stellar objects. A variety of pulsating variables allows us to test various parameters of micro- and macrophysics by means of oscillation data. I will review the most outstanding key problems, both observational and theoretical, of which our knowledge can be improved by means of asteroseismology.

Binary Source Lensing and the Repeating OGLE EWS Events

A microlensing event may exhibit a second brightening when the source and/or the lens is a binary star. Previous study revealed 19 such repeating event candidates among 4120 investigated microlensing light curves of the Optical Gravitational Lensing Experiment (OGLE). The same study gave the probability ~ 0.0027 for a repeating event caused by a binary lens. We present the simulations of binary source lensing events and calculate the probability of observing a second brightening in the light curve. Applying to simulated light curves the same algorithm as was used in the analysis of real OGLE data, we find the probability ~ 0.0018 of observing a second brightening in a binary source lensing curve. The expected and measured numbers of repeating events are in agreement only if one postulates that all lenses and all sources are binary. Since the fraction of binaries is believed to be <= 50%, there seems to be a discrepancy.

Constraints on the High-Density Nuclear Equation of State from Neutron Star Observables

Depending on the density reached in the cores of neutron stars, such objects may contain stable phases of novel matter found nowhere else in the Universe. This article gives a brief overview of these phases of matter and discusses astrophysical constraints on the high-density equation of state associated with ultra-dense nuclear matter.

Masses of Black Holes in the Universe

The different methods of determination of black holes (BHs) masses are presented for three classes of BHs observed in the Universe: stellar mass BHs, intermediate mass BHs (IMBHs) and supermassive BHs (SBHs). The results of these determinations are briefly reviewed: stellar mass BHs are found in the range of about 3 to about 20 solar masses, IMBHs in the range of a few hundreds to a few tens of thousands solar masses (the determinations are much less precise for these objects) and SBHs in the range of about 3x10^5 to about 6x10^10 solar masses.

Identifying pulsation modes from two-passband photometry

I discuss a prospect for mode identification from two-passband photometry of forthcoming BRITE space mission. Examples of photometric diagnostic diagrams are shown for three types of main sequence pulsating variables: $beta$ Cephei, Slowly Pulsating B-type and $delta$ Scuti stars. I consider also taking into account the radial velocity data from simultaneous spectroscopy, which can be carried out from the ground. With such observations, much better discrimination of the spherical harmonic degree, $ell$, can be accomplished and more constraints on stellar parameters and input physics can be derived.