Questions tagged [topological-defects]

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Can cosmological defects escape a black hole?

Based on my understanding, anything that can't move faster than light can't get out of a black hole, but space can since it can move faster than light (hence cosmic inflation is exponentiated). Also, ...
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More rigorous explanation as to why $G/H = G'/H'$ for vacuum manifolds?

When studying topological defects, the parameter space (or vacuum manifold in QFT) is denoted as the coset space $G/H$, where $G$ corresponds to the symmetry group of the Lagrangian and $H$ the ...
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Is an electron a topological defect? [duplicate]

Magnetic monopoles such as the t'Hooft Polyakov monopoles are special field configurations within some SU(2) gauge theory, that are characterised by their non trivial topology, thus calling them one ...
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Defect network in conformal field theory and topological field theory?

Recently, I am trying to read the paper Generalized Global Symmetries. In the Preliminaries part, authors formulated ordinary symmetries by network of defects (PP6-7). It seems to be related to ...
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Is the phenomenon of geometrical frustration in condensed matter physics related to some kind of topological invariant?

Edit (attempt to clarify my question a little bit): I’m not thinking geometrical frustration should be necessarily associated to a topological invariant in a direct way, but maybe local geometrical ...
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Cosmic strings, domain walls, and magnetic monopoles are topological defects, but what's defecting?

Wikipedia gives an explanation of cosmic strings that I'm sure would be very helpful if I had a major in topology, but alas I do not. I know that a topological defect is any sort of discontinuity in a ...
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Dislocation Jogs and kinks

When two dislocations interact, it creates a step which is known as jogs (if it is from two different slip planes) or kinks (if it is in the same slip plane). My confusion is, why it is like a step? ...
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Spacetime with a point defect

What is the metric for a spacetime with a point defect? Spacetime metric with line defects are well-known, they are basically Cosmic strings. Is anyone aware of an example for spacetime with point ...
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In a nutshell explanation of topological defects and charge?

I read this great answer: What is a topological defect? in which it seems that a topological defect is a region of the domine of a function in which the function is not defined. In fact, here it is ...
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Homotopy group for spin-1 BEC

Homotopy group can be used to classify topological defects. The procedure is Find the Lie group $G$ that leaves the free-energy functional invariant when transforming $\psi$, where $\psi$ is the ...
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Topological defects in general and Chern-Simons in particular

I'm trying to gain intuition on some physical concepts that I cannot yet fully understand, and I think many of you can help me. Is it correct to think of of a topological defect as the addition ad hoc ...
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Topological spin in $Z_2$ toric code

On page 20 of this paper, Kitaev shows that the composite particle $\varepsilon = e \times m$ is a fermion. He also said that it is easy to show $e$ is a boson (i.e. carries a topological spin of 1). ...
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Generator of conformal transformation in presence of conformal defect

I was reading about conformal defects, when I came across the following: Consider some free massless scalar field in 1+1 dimension $\phi(x,t)$ living on a world sheet seperated by some defect at $x=0$...
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How to create a cosmic string?

I know about cosmic strings. They are 1-D topological defects in space-time which may had been created during the symmetry breaking phase transition during the big bang. But my question is : Are ...
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Deforming a nematic line defect to a uniform configuration

In Nakahara section 4.9, "Defects in nematic liquid crystals", it is discussed that the order parameter for a nematic should be the real projective plane $\mathbb{R}P^2$, which has ...
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Why are electric monopoles not interpreted as topological defects but magnetic monopoles are?

What explains this asymmetry between the electric and magnetic fields if both electric and magnetic monopoles exist? Can't Maxwell's equations be formulated to be symmetric between the two in the ...
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What is the gravitational force between monopoles?

Domain walls have the unusual property that they are gravitationally repulsive (See reviews by Sikivie). Does a similarly strange result hold for monopoles?
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Sum of topological charges is the Euler characteristic

I have seen many places claiming that the given a collection of topological defects on a 2-dimensional surface, the sum of the topological charges is $2\pi\chi$ (where $\chi$ is the Euler ...
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Is there a difference between topological defects and topological soliton?

Is there a difference between topological defects and topological soliton? Or are these objects the same thing? I ask this because it very common find some papers whose the authors itself refer, for ...
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Does the Standard Model have texture defects?

In the standard classification of topological defects, in a theory with vacuum manifold $\mathcal{M}$, $\pi_0(\mathcal{M})$ corresponds to domain walls, $\pi_1(\mathcal{M})$ corresponds to strings/...
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What's the origin of the vortex's ansatz $\phi\big(\vec{x}\big)=f\big(r\big)e^{-in\theta}$?

What's the origin of the vortex's ansatz $\phi\big(\vec{x}\big)=f\big(r\big)e^{-in\theta}$ in the de Vega and Schaposnik paper? In their article Classical vortex solution of the Abelian Higgs model,...
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What is a String Wall?

This question has nothing to do with sound waves, physical strings or walls... I am reading: https://arxiv.org/abs/1709.07091 It states "In the post-inflationary PQ symmetry breaking scenario, ...
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Topological solitons in general dimension

Let's begin with a simple model of a field theory: $$ \mathcal{H} = \int ( \nabla \phi ) ^2 $$ where $\phi$ is an angle valued field defined on some space. We suppose for the moment to freeze out ...
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What is a dislocation defect in metals as opposed to a grain boundary?

Almost all metals found in nature are polycrystalline so that there must be grain boundaries. My understanding is that individual grains are tiny defectless crystals and different grains are rotated w....
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Skyrmion of pseudo-scalar mesons and vector mesons

I had heard statements that Skyrmion of pions (pseudo-scalar mesons) cannot be an object like baryon, however, Skyrmion of vectors mesons may indeed form an object like baryon. For example, see this ...
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6 votes
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Non-chiral skyrmion v.s. Left/Right chiral skyrmion

A skyrmion in a 3-dimensional space (or a 3-dimensional spacetime) is detected by a topological index $$n= {\tfrac{1}{4\pi}}\int\mathbf{M}\cdot\left(\frac{\partial \mathbf{M}}{\partial x}\times\frac{...
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