Leading Infrared Logarithms from Unitarity, Analyticity and Crossing

We derive non-linear recursion equations for the leading infrared logarithms in massless non-renormalizable effective field theories. The derivation is based solely on the requirements of the unitarity, analyticity and crossing symmetry of the amplitudes. That emphasizes the general nature of the corresponding equations. The derived equations allow one to compute leading infrared logarithms to essentially unlimited loop order without performing a loop calculation. For the implementation of the recursion equation one needs to calculate tree diagrams only. The application of the equation is demonstrated on several examples of effective field theories in four and higher space-time dimensions.Comment: 12 page

Evolution of Cosmic Necklaces and Lattices

Previously developed analytic models for the evolution of cosmic string and monopole networks are applied to networks of monopoles attached to two or more strings; the former case is usually known as cosmic necklaces. These networks are a common consequence of models with extra dimensions such as brane inflation. Our quantitative analysis agrees with (and extends) previous simpler estimates, but we will also highlight some differences. A linear scaling solution is usually the attractor solution for both the radiation and matter-dominated epochs, but other scaling laws can also exist, depending on the universe's expansion rate and the network's energy loss mechanisms.Comment: 4 page

Research of the stress-strain state of rods obtained by porous blank extrusion

The features of the stress-strain state in the cross section of rods under forming are revealed by the finite element modeling of the process of direct extrusion of a porous iron blank. In particular, the nature of porosity distribution and the stress-state stiffness coefficient obtained as a result of calculating the residual stresses field in the rod is studied. The Gurson-Tvergaard-Needleman (GTN) model is used to describe the behavior of the material of a porous blank under plastic deformation. It has been established that, in different cross-section zones of the rod, the values of the stress-state coefficient can be either positive or negative. It is shown that the most unfavorable area of the cross-section in the drawing index range investigated (2.04-4) is the material layer lying in the immediate vicinity of the outer surface of the rod (0.7...0.8R, where R is the rod radius), where the localization of tensile stresses is observed which promotes the emergence and growth of layered annular cracks. © 2017 Author(s)

Colloquium : disclination loops, point defects, and all that in nematic liquid crystals

The homotopy theory of topological defects is a powerful tool for organizing and unifying many ideas across a broad range of physical systems. Recently, experimental progress was made in controlling and measuring colloidal inclusions in liquid crystalline phases. The topological structure of these systems is quite rich but, at the same time, subtle. Motivated by experiment and the power of topological reasoning, the classification of defects in uniaxial nematic liquid crystals was reviewed and expounded upon. Particular attention was paid to the ambiguities that arise in these systems, which have no counterpart in the much-storied XY model or the Heisenberg ferromagnet

Magnetic Monopoles in Field Theory and Cosmology

The existence of magnetic monopoles is predicted by many theories of particle physics beyond the Standard Model. However, in spite of extensive searches, there is no experimental or observational sign of them. I review the role of magnetic monopoles in quantum field theory and discuss their implications for particle physics and cosmology. I also highlight their differences and similarities with monopoles found in frustrated magnetic systems, and discuss how experiments carried out in these systems could help us understand the physics of fundamental monopoles.Comment: 15 pages, no figures. Based on a talk given at the discussion meeting "Emergent magnetic monopoles in frustrated magnetic systems" at the Kavli Royal Society International Centre, 17-18 October 2011. To be published in Philosophical Transactions of the Royal Society

The Hopf Skyrmion in QCD with Adjoint Quarks

We consider a modification of QCD in which conventional fundamental quarks are replaced by Weyl fermions in the adjoint representation of the color SU(N). In the case of two flavors the low-energy chiral Lagrangian is that of the Skyrme-Faddeev model. The latter supports topologically stable solitons with mass scaling as N^2. Topological stability is due to the existence of a nontrivial Hopf invariant in the Skyrme-Faddeev model. Our task is to identify, at the level of the fundamental theory, adjoint QCD, an underlying reason responsible for the stability of the corresponding hadrons. We argue that all "normal" mesons and baryons, with mass O(N^0), are characterized by (-1)^Q (-1)^F =1, where Q is a conserved charge corresponding to the unbroken U(1) surviving in the process of the chiral symmetry breaking (SU(2) \to U(1) for two adjoint flavors). Moreover, F is the fermion number (defined mod 2 in the case at hand). We argue that there exist exotic hadrons with mass O(N^2) and (-1)^Q (-1)^F = -1. They are in one-to-one correspondence with the Hopf Skyrmions. The transition from nonexotic to exotic hadrons is due to a shift in F, namely F \to F - {\cal H} where {\cal H} is the Hopf invariant. To detect this phenomenon we have to extend the Skyrme-Faddeev model by introducing fermions.Comment: 18 pages, 3 figures; v.2: a reference and a comment added; v.3: two comments added, figures improve

Non-Abelian Vortex-String Dynamics from Nonlinear Realization

The dynamics of the non-Abelian vortex-string, which describes its low energy oscillations into the target $D=3+1$ spacetime as well as its orientations in the internal space, is derived by the approach of nonlinear realization. The resulting action correlating these two sectors is found to have an invariant synthesis form of the Nambu-Goto-${\bf C}P^{N-1}$ model actions. Higher order corrections to the vortex actions are presented up to the order of quartic derivatives. General $p$-brane dynamics in terms of the internal symmetry breaking is also discussed.Comment: 30 page