Assuming the Lorentz and CPT invariances we show that neutron-antineutron oscillation implies breaking of CP along with baryon number violation -- i.e. two of Sakharov conditions for baryogenesis. The oscillation is produced by the unique operator in
the effective Hamiltonian. This operator mixing neutron and antineutron preserves charge conjugation C and breaks P and T. External magnetic field always leads to suppression of oscillations. Its presence does not lead to any new operator mixing neutron and antineutron.
We study N=(0,2) deformed (2,2) two-dimensional sigma models. Such heterotic models were discovered previously on the world sheet of non-Abelian strings supported by certain four-dimensional N=1 theories. We study geometric aspects and holomorphic pr
operties of these models, and derive a number of exact expressions for the beta functions in terms of the anomalous dimensions analogous to the NSVZ beta function in four-dimensional Yang-Mills. Instanton calculus provides a straightforward method for the derivation. The anomalous dimensions are calculated up to two loops implying that one of the beta functions is explicitly known up to three loops. The fixed point in the ratio of the couplings found previously at one loop is not shifted at two loops. We also consider the N=(0,2) supercurrent supermultiplet (the so-called hypercurrent) and its anomalies, as well as the Konishi anomaly. This gives us another method for finding exact $beta$ functions. We prove that despite the chiral nature of the models under consideration quantum loops preserve isometries of the target space.
The general problem of a perfect incompressible fluid motion with vortex areas and variant constant vorticities is formulated. The M.A. Goldshtiks variational approach is considered on research of dual problems for flows with vortex and potential are
as that describe detached flow and a motion model of a perfect incompressible fluid in field of Coriolis forces.
In this work there are considered model problems for two nonlinear equations, which type depends on the solution. One of the equations may be called a nonlinear analog of the Lavrentev-Bitsadze equation.
We investigate Poisson properties of Postnikovs map from the space of edge weights of a planar directed network into the Grassmannian. We show that this map is Poisson if the space of edge weights is equipped with a representative of a 6-parameter fa
mily of universal quadratic Poisson brackets and the Grasmannian is viewed as a Poisson homogeneous space of the general linear group equipped with an appropriately chosen R-matrix Poisson-Lie structure. We also prove that Poisson brackets on the Grassmannian arising in this way are compatible with the natural cluster algebra structure.
Many stormy events in astrophysics occur due to the sudden magnetic energy release. This is possible if a magnetic configuration abruptly changes its topology, an event usually referred to as magnetic reconnection. It is known that pure Ohmic decay i
s inefficient, occurring during cosmological times (due to the huge characteristic scales $L$). It is recognized that the presence of current sheets speeds up the process, but still insufficiently$^{1,2,3,4,5}$. We show that, in highly compressible and substantially gravitational media, the reconnection is fast enough to account for stormy events. Thus, highly compressible situations offer exiting opportunities in explanations of violent events, although full-scale compressible and gravitational simulations proved to be quite challenging.
The chiral symmetry of QCD shows up in the linear Weyl--Wigner mode at short Euclidean distances or at high temperatures. On the other hand, low-lying hadronic states exhibit the nonlinear Nambu--Goldstone mode. An interesting question was raised as
to whether the linear realization of the chiral symmetry is asymptotically restored for highly excited states. We address it in a number of ways. On the phenomenological side we argue that to the extent the meson Regge trajectories are observed to be linear and equidistant, the Weyl--Wigner mode is not realized. This picture is supported by quasiclassical arguments implying that the quark spin interactions in high excitations are weak, the trajectories are linear, and there is no chiral symmetry restoration. Then we use the string/gauge duality. In the top-down Sakai--Sugimoto construction the nonlinear realization of the chiral symmetry is built in. In the bottom-up AdS/QCD construction by Erlich et al., and Karch et al. the situation is more ambiguous. However, in this approach linearity and equidistance of the Regge trajectories can be naturally implemented, with the chiral symmetry in the Nambu--Goldstone mode. Asymptotic chiral symmetry restoration might be possible if a nonlinearity (convergence) of the Regge trajectories in an intermediate window of $n,J$, beyond the explored domain, takes place. This would signal the failure of the quasiclassical picture.
