In mathematics and physics, a topological defect is a solution of a system of partial differential equations or of a quantum field theory homotopically distinct from the vacuum solution.
Questions tagged [topological-defects]
45 questions
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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/vortices,
$\pi_2(\mathcal{M})$ corresponds to…
knzhou
- 107,105
9
votes
2 answers
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 frustration behaviour correlates to one globally,…
dahemar
- 2,513
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votes
2 answers
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
$$n= {\tfrac{1}{4\pi}}\int\mathbf{M}\cdot\left(\frac{\partial \mathbf{M}}{\partial x}\times\frac{\partial \mathbf{M}}{\partial y}\right)dx dy
$$…
wonderich
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2 answers
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 presence of both monopoles? What leads to magnetic…
4
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Is an electron a topological defect?
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 instance of a topological defect. Electrons…
2000mg Haigo
- 791
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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 constructing a modular invariant CFT partition…
Ruizhi liu
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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 example, the domain wall's, monopoles, cosmic…
lucenalex
- 387
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1 answer
Topological defects in terms of homotopy classes of maps between spheres
I have some troubles with understanding the concept of topological defects and their treatise via homotopy groups of spheres as discussed in wikipedia article. More precisely,
if we encode these in terms of different (pointed) homotopy classes…
user267839
- 1,711
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0 answers
Soliton and Goldstone boson
I'm learning Gross-Pitaevskii model. By spontaneous symmetry breaking one obtains Bogoljubov modes, which ensures Landau criterion. So those modes have two features, for one they are Goldstone bosons corresponding to spontaneous symmetry breaking of…
JinH
- 146
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Gauging a finite non-abelian global symmetry in 2D
Consider a 2D system with a non-anomalous finite non-abelian global symmetry $G$, for example $$G = S_3=\{e,a,a^2,b,ab,a^2b\}$$ with $a^3=b^2=1$. One expects the local operators charged under the symmetry $S_3$ should transform under some…
JQ Skywalker
- 189
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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 written that
Topological defects are parts of the…
Aesku
- 391
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0 answers
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, de Vega and Schaposnik state that the…
lucenalex
- 387
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1 answer
Cosmic Strings as Topological Defects (heuristics)
I have a lot of troubles to understand heuristically the principle behind Kibble's model for genesis of cosmic strings via Kibble mechanism. More precisely I not understand how to interpret following two pictures I found here:
Prelude: We start…
user267839
- 1,711
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votes
1 answer
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 medium that's hard to remove. Things I know are…
zucculent
- 1,473
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0 answers
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). I am having trouble proving this result. What…
Waterfall
- 538