Related papers: Formation of Topological Defects
The scenario of a cosmology with topological defects is surveyed starting from the field theoretic aspects and ending with a description of large-scale structure formation and magnetic field generation. (Lectures delivered at ICTP, Trieste,…
Higher-form symmetries are a valuable tool for classifying topological phases of matter. However, emergent higher-form symmetries in interacting many-body quantum systems are not typically exact due to the presence of topological defects.…
Current theories of particle physics lead to the unavoidable conclusion that there must have been several phase transitions in the early universe. Further, in the context of these theories, it is possible that cosmological phase transitions…
In the first one of these two lectures, I give an introductory review of phase transitions in finite temperature field theories. I highlight the differences between theories with global and local symmetries, and the similarities between…
These lectures review certain topological defects and aspects of their cosmology. Unconventional material includes brief descriptions of electroweak defects, the structure of domain walls in non-Abelian theories, and the spectrum of…
We discuss formation of cosmic strings associated with a spontaneously broken approximate $U(1)$ symmetry by performing classical field-theoretical simulations. An original $U(1)$ symmetry is explicitly broken down to its subgroup $Z_N$…
There are two prominent applications of the mathematical concept of topology to the physics of materials: band topology, which classifies different topological insulators and semimetals, and topological defects that represent immutable…
Domain walls, strings and monopoles are extended objects, or defects, of quantum origin with topologically non--trivial properties and macroscopic behavior. They are described in Quantum Field Theory in terms of inhomogeneous condensates.…
When a symmetry gets spontaneously broken in a phase transition, topological defects are typically formed. The theoretical picture of how this happens in a breakdown of a global symmetry, the Kibble-Zurek mechanism, is well established and…
We study spontaneous symmetry breakings for fermions (spinless and spinful) on a two-dimensional kagome lattice with nearest-neighbor repulsive interactions in weak coupling limit, and focus in particular on topological Mott insulator…
We examine simulations of the formation of domain walls, cosmic strings, and monopoles on a cubic lattice, in which the topological defects are assumed to lie at the zeros of a piecewise constant 1, 2, or 3 component Gaussian random field,…
We discuss the structure of topological defects in the context of extra dimensions where the symmetry breaking terms are localized. These defects develop structure in the extra dimension which differs from the case where symmetry breaking…
If Lorentz symmetry is broken, it must have occurred dynamically, via a vector or tensor field whose potential energy forces it to take on a non-zero background expectation value "in vacuum". If the set of minima of this potential (the…
Topological defects, in particular cosmic strings, give rise to an interesting mechanism for generating the primordial perturbations in the early Universe which are required to explain the present structure. An overview of the cosmic string…
Kinks, vortices, monopoles are extended objects, or defects, of quantum origin with topologically non-trivial properties and macroscopic behavior. They are described in Quantum Field Theory in terms of non-homogeneous boson condensation. I…
Topological defects are common in many everyday systems. In general, they appear if a symmetry is broken at a rapid phase transition. In this article, I explain why it is believed that they should have also been formed in the early universe…
We propose a class of field theories featuring solitonic solutions in which topological defects can end when they intersect other defects of equal or higher dimensionality. Such configurations may be termed ``Dirichlet topological…
Superconductors are the only experimentally accessible systems with spontaneously broken gauge symmetries which support topologically nontrivial defects, namely string defects. We propose two experiments whose aim is the observation of the…
We show that the process of spontaneous symmetry breaking can trap a field theoretic system in a highly non-trivial state containing a lattice of domain walls. In one large compact space dimension, a lattice is inevitably formed. In two…
We examine the interplay of symmetry and topological order in $2+1$ dimensional topological phases of matter. We present a definition of the \it topological symmetry \rm group, which characterizes the symmetry of the emergent topological…