Topological structures on domain walls

The possibility that a symmetry which is preserved in the vacuum might be broken in the interior of a domain wall is discussed. The simplest field theory example is explored in detail. The possibility that unexpected topological structures could then arise is illustrated with some examples. If the broken symmetry is electromagnetism, the domain wall becomes superconducting, a phenomenon which was discovered in the context of cosmic strings.     

Skyrmions from instantons inside domain walls

Some years ago, Atiyah and Manton described a method to construct approximate Skyrmion solutions from Yang-Mills instantons. Here we present a dynamical realization of this construction using domain walls in a five-dimensional gauge theory. The non-Abelian gauge symmetry is broken in each vacuum but restored in the core of the domain wall, allowing instantons to nestle inside the wall. We show that the world volume dynamics of the wall is given by the Skyrme model, including the four-derivative term, and the instantons appear as domain wall Skyrmions.     

Topological defects in cosmology

Present status of theories of topological defects in particle theory models of the early Universe is discussed. Various consequences of topological defects in cosmology, such as constraints on particle theory models, structure formation etc. are discussed.     

Topological defects in CFT

Areview of the notion, properties and the use of topological defects in 2d conformal field theories is presented. An emphasis is made on the recent interpretation of such operators in non-rational theories, as describing Wilson-’t Hooft loop operators of N = 2 supersymmetric 4d topological theories.     

Topological defects and cosmology

Many particle physics models of matter admit solutions corresponding to stable or long-lived topological defects. In the context of standard cosmology it is then unavoidable that such defects will form during phase transitions in the very early Universe. Certain types of defects lead to disastrous consequences for cosmology, others may play a useful role, as possible seeds for the formation of structure in the Universe, or in mediating baryon number violating processes. In all cases, topological defects lead to a fruitful interplay between particle physics and cosmology.     

Topological defects in contracting universes

We study the behavior and consequences of cosmic string networks in contracting universes. They approximately behave during the collapse phase as radiation fluids. Scaling solutions describing this are derived and tested against high-resolution numerical simulations. A string network in a contracting universe, together with the gravitational radiation it generates, can affect the dynamics of the universe both locally and globally and be an important source of radiation, entropy, and inhomogeneity. We discuss possible implications for bouncing and cyclic models.     

Topological defects in superfluid helium

Some aspects of classical field-theoretic phenomenology of superfluid helium are presented.     

Topological defects with long-range interactions

We investigate a modified sine-Gordon equation which possesses soliton solutions with long-range interaction. We introduce a generalized version of the Ginzburg-Landau equation which supports long-range topological defects in D = 1 and D > 1. The interaction force between the defects decays so slowly that it is possible to enter the non-extensivity regime. These results can be applied to non-equilibrium systems, pattern formation and growth models.     

Topological defects in spherical nematics

We study the organization of topological defects in a system of nematogens confined to the two-dimensional sphere (S2). We first perform Monte Carlo simulations of a fluid system of hard rods (spherocylinders) living in the tangent plane of S2. The sphere is adiabatically compressed until we reach a jammed nematic state with maximum packing density. The nematic state exhibits four +1/2 disclinations arrayed on a great circle. This arises from the high elastic anisotropy of the system in which splay (K1) is far softer than bending (K3). We also introduce and study a lattice nematic model on S2 with tunable elastic constants and map out the preferred defect locations as a function of elastic anisotropy. We find a one-parameter family of degenerate ground states in the extreme splay-dominated limit K_{3}/K_{1}-->infinity. Thus the global defect geometry is controllable by tuning the relative splay to bend modulus.     

Leptogenesis with left-right domain walls

The presence of domain walls separating regions of unbrokenSU(2)_L andSU(2)_R is shown to provide necessary conditions for leptogenesis which converts later to the observed baryon asymmetry. The strength of lepton number violation is related to the Majorana neutrino mass and hence related to current bounds on light neutrino masses. Thus the observed neutrino masses and the baryon asymmetry can be used to constrain the scale of left-right symmetry breaking.     

Cosmic strings and domain walls

Phase transitions in the early universe can give rise to microscopic topological defects: vacuum domain walls, strings, walls bounded by strings, and monopoles connected by strings. This article reviews the formation, physical properties and the cosmological evolution of various defects. A particular attention is paid to strings and their cosmological consequences, including the string scenario of galaxy formation and possible observational effects of strings.     

New massive gravity domain walls

The properties of the asymptotic AdS₃${\mathit{AdS}}_3$ space–times representing flat domain walls (DW's) solutions of the new massive 3D gravity with scalar matter are studied. Our analysis is based on first order BPS-like equations involving an appropriate superpotential. The Brown–York boundary stress-tensor is used for the calculation of DW's tensions as well as of the CFT₂${\mathit{CFT}}_2$ central charges. The holographic renormalization group flows and the phase transitions in specific deformed CFT₂${\mathit{CFT}}_2$ dual to 3D massive gravity model with quadratic superpotential are discussed.     

Topological classification of unknotted ring defects

Unknotted ring defects in ordered media are classified in terms of the homotopy theory. It is also investigated what type of point defects will appear when a radius of the ring defect tends to zero.     

Topological defects dynamics and Melnikov's theory

We use Melnikov's analysis to construct recurrence time maps near homoclinic and heteroclinic bifurcations. We show that a method developed by Kawasaki and Ohta in order to study defects dynamics is indeed equivalent to this version of Melnikov's theory.