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Questions tagged [topological-defects]

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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 ...
JinH's user avatar
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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 ...
JQ Skywalker's user avatar
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Energy of Domain Wall in field theory

It is well known that in the case of the Mexican hat potential in $D=(1+1)$, it is possible to find kink solutions that interpolate between the vacua of the theory. In the context of cosmology, these ...
Lucky Charms's user avatar
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Axion domain wall number and heavy quarks

The domain wall number of a UV complete theory of axion is related to the number of PQ-charged heavy quarks that run in the loop. In the case of KSVZ model, $N_{\rm DW}=1$ while in DFSZ, $N_{\rm DW}&...
PhysicsStudy's user avatar
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Cosmic string in real space

I am considering $U(1)$ global cosmic string. In the case of wine-bottle potential with real field ($\phi$), it is known that there exists a static solution that corresponds to cosmic string (or ...
PhysicsStudy's user avatar
1 vote
1 answer
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Topological charge of angle field

I want to numerically calculate the topological charge using a 2D angle field defined on a rectangular grid. At each vertex of the grid, a value of angle is defined. Now, I want to calculate the ...
vinayv's user avatar
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1 answer
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What is a symmetry defect?

I found that it is a normal concept appearing in condensed matter physics and especially topological order field. I have been aware of the topological defect. But what is a symmetry defect? Could ...
user35734's user avatar
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1 answer
168 views

Dimensionality of state space of TQFTs

As the title suggests, I am wondering about the dimensionality of state spaces in $d$-dimensional TQFTs. As of yet I have mostly been concerned with the mathematical, functorial definition of TQFTs as ...
Topological Sigma Grindset's user avatar
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Are branes topological defects? How else could they be physical?

As far as I understand, the branes of brane cosmology are lower-dimensional "sub-manifolds" of some space. It was hard to imagine for me how such structure could exist and be physical. But ...
M. Winter's user avatar
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0 answers
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Could the universe be a topological defect in a higher space?

I am a mathematician with an undergrad understanding of physics. I recently learned of topological defects in quantum fields. It is an intriguing idea that there could be regions in our universe that, ...
M. Winter's user avatar
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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 ...
user267839's user avatar
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Can dark matter be explained by defects of spacetime?

Dark matter is believed to be a substance of unknown origin with mass that is distributed in space. Can the same observed effects be explained by an intrinsic curvature of regions of space without ...
Trident D'Gao's user avatar
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How do you calculate the partition function on a manifold-with-corners in extended TQFT?

In Atiyah's formulation, a Topological Quantum Field Theory (TQFT), is a functor $Z:d\text{Bord}\to\text{Hilb}$. That is, $Z$ assigns: \begin{align} \text{Closed compact $(d-1)$-manifolds} &\to \...
nodumbquestions's user avatar
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How do defects in a superconducting nanostructure affect the supercurrent?

I was wondering how point defects in a superconducting nanowire affect the supercurrent flowing through this wire. In a naive view I am expecting the defect to decrease the maximum current allowed in ...
Fabian's user avatar
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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, ...
Prido1024's user avatar
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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 ...
2000mg Haigo 's user avatar
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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 ...
2000mg Haigo 's user avatar
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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 ...
Ruizhi liu's user avatar
9 votes
2 answers
411 views

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 ...
dahemar's user avatar
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1 vote
1 answer
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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 ...
zucculent's user avatar
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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? ...
an_idiot_noob's user avatar
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1 answer
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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 ...
Dr. user44690's user avatar
3 votes
1 answer
389 views

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 ...
Ali Esquembre Kucukalic's user avatar
0 votes
1 answer
81 views

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 ...
Hao's user avatar
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1 vote
1 answer
142 views

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 ...
Rebour's user avatar
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0 answers
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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). ...
Waterfall's user avatar
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2 votes
1 answer
114 views

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 $x=0$...
Ramsey's user avatar
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1 vote
0 answers
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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 ...
Rounak Sarkar's user avatar
2 votes
1 answer
191 views

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 ...
Kai's user avatar
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5 votes
2 answers
441 views

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 ...
Anthony Khodanian's user avatar
2 votes
1 answer
129 views

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?
user avatar
1 vote
1 answer
180 views

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 ...
Chetan Vuppulury's user avatar
4 votes
1 answer
261 views

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 ...
lucenalex's user avatar
  • 387
10 votes
1 answer
381 views

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/...
knzhou's user avatar
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3 votes
0 answers
232 views

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,...
lucenalex's user avatar
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2 votes
1 answer
203 views

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, ...
Rick's user avatar
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2 votes
0 answers
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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 ...
MrRobot's user avatar
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1 vote
1 answer
180 views

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....
Solidification's user avatar
2 votes
1 answer
121 views

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 ...
wonderich's user avatar
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7 votes
2 answers
1k views

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{...
wonderich's user avatar
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