Fermions, Monopoles & Quantum Hall: New Advances

[mitchell porter]

Two papers today:

https://arxiv.org/abs/2103.13639
Missing final state puzzle in the monopole-fermion scattering
Ryuichiro Kitano, Ryutaro Matsudo
[Submitted on 25 Mar 2021]

It has been known that when a charged fermion scatters off a monopole, the fermion in the s-wave component must flip its chirality, i.e., fermion number violation must happen. This fact has led to a puzzle; if there are two or more flavors of massless fermions, any superposition of the fermion states cannot be the final state of the s-wave scattering as it is forbidden by conservation of the electric and flavor charges. The unitary evolution of the state vector, on the other hand, requires some interpretation of the final states. We solve the puzzle by finding new particle excitations in the monopole background, where multi-fermion operators exhibit condensation. The particles are described as excitations of closed-string configurations of the condensates.

https://arxiv.org/abs/2103.13574
Quark-Gluon Plasma and Nucleons a la Laughlin
Wei Lu
[Submitted on 25 Mar 2021]

Inspired by Laughlin's theory of the fractional quantum Hall effect, we propose a wave function for the quark-gluon plasma and the nucleons. In our model, each quark is transformed into a composite particle via the simultaneous attachment of a spin monopole and an isospin monopole. This is induced by the mesons endowed with both spin and isospin degrees of freedom. The interactions in the strongly-correlated quark-gluon system are governed by the topological wrapping number of the monopoles, which is an odd integer to ensure that the overall wave function is antisymmetric. The states of the quark-gluon plasma and the nucleons are thus uniquely determined by the combination of the monopole wrapping number m and the total quark number N. The radius squared of the quark-gluon plasma is expected to be proportional to mN. We anticipate the observation of such proportionality in the heavy ion collision experiments.

The first paper is a new detail of the "Callan-Rubakov effect", known since the early 1980s, in which conservation laws can be broken when a charged fermion scatters off a GUT monopole. A recent (2018) model of single-flavor baryons as a membrane ("pancake") bounded by a string, turns out to clarify a previously obscure aspect of the Callan-Rubakov dynamics. It's always nice when a theoretical innovation obtains unintended validation from a completely different application.

The second paper is more exotic. The author is proposing a new model of strongly interacting systems - not just the quark-gluon plasma, but also hadrons in general. In his model, each quark has a "spin monopole" and "isospin monopole" attached, which are topological solitons formed from a new "spin-isospin" meson field, represented using a Clifford algebra, something unusual for QCD... I emphasize that the author is not replacing QCD, but instead claiming that this is a valid approximation to the opaque dynamics of the strong interaction.

Curiously, along with monopoles, the papers have one more thing in common: the quantum Hall effect is in the background of both. The membranes of the first paper were introduced in 2018 as "quantum Hall droplets", and the new model of the second paper is inspired by Laughlin's quasiparticle model of the fractional quantum Hall effect.

 

[mitchell porter]

https://arxiv.org/abs/2109.01145
Monopoles Entangle Fermions
Csaba Csáki, Yuri Shirman, Ofri Telem, John Terning
[Submitted on 2 Sep 2021]

We resolve the decades old mystery of what happens when a positron scatters off a minimal GUT monopole in an s-wave, first discussed by Callan in 1983. Using the language of on-shell amplitudes and pairwise helicity we show that the final state contains two up quarks and a down quark entangled with angular momentum stored in the gauge fields, which is the only particle final state that satisfies angular momentum and gauge charge conservation. The cross section for this process is as large as in the original Rubakov-Callan effect, only suppressed by the QCD scale. The final state we find cannot be seen in Callan's truncated 2D theory, since our entanglement requires more than 2 dimensions.

I had to mention this new paper since it contradicts the first paper mentioned above. For now I express no opinion on who's right.

 

[mitchell porter]

https://arxiv.org/abs/2306.07318
Monopoles, Scattering, and Generalized Symmetries
Marieke van Beest, Philip Boyle Smith, Diego Delmastro, Zohar Komargodski, David Tong

We reconsider the problem of electrically charged, massless fermions scattering off magnetic monopoles. The interpretation of the outgoing states has long been a puzzle as, in certain circumstances, they necessarily carry fractional quantum numbers. We argue that consistency requires such outgoing particles to be attached to a topological co-dimension 1 surface, which ends on the monopole. This surface cannot participate in a 2-group with the magnetic 1-form symmetry and is often non-invertible. Equivalently, the outgoing radiation lies in a twisted sector and not in the original Fock space. The outgoing radiation therefore not only carries unconventional flavor quantum numbers, but is often trailed by a topological field theory [...]

I mention this paper for a few reasons. First, I recognize two of the authors, Zohar Komargodski and David Tong, as two quite accomplished contemporary field theorists. Second, the analysis involves some of the hottest new concepts in recent field theory, "higher symmetries" and "non-invertible symmetries". Third, it's weird that to describe particle scattering, you'd have to extend your original Hilbert space (by including some extra topological observables). I haven't yet got the hang of what non-invertible symmetries are about, maybe it's time I did.

 

[kodama]

do Monopoles exist

 

[mitchell porter]

do Monopoles exist

They might, they're a generic prediction of grand unified theories. Also, field configurations described as monopoles occur even in the gauge theories of the standard model. I have not been able to find a precise definition, but they seem to be virtual topological objects that occur in the Euclidean path integral. It has been suggested that quark confinement is due to condensation of these "QCD monopoles".

 

[kodama]

They might, they're a generic prediction of grand unified theories. Also, field configurations described as monopoles occur even in the gauge theories of the standard model. I have not been able to find a precise definition, but they seem to be virtual topological objects that occur in the Euclidean path integral. It has been suggested that quark confinement is due to condensation of these "QCD monopoles".

why'd so hard to discover

 

[ohwilleke]

do Monopoles exist

The papers you cite are strong theoretical evidence that monopoles do not exist.

 

[Vanadium 50]

why'd so hard to discover

In general, it's hard to discover what isn't there.

 

[kodama]

In general, it's hard to discover what isn't there.

since t, they're a generic prediction of grand unified theories are they falsified ?

 

[Vanadium 50]

If you mean 't Hooft–Polyakov, the fact that something is permitted in GUTs does not mean that is required.

 

[ohwilleke]

since t, they're a generic prediction of grand unified theories are they falsified ?

GUTs that predict monopoles are theoretically strongly disfavored. And, observationally, GUTs that predict proton decay are also strongly disfavored. These are some important reasons why GUT theories are a lot less popular now than they used to be.

 

[mitchell porter]

OK, a few comments on this discussion of monopoles, which is equivocating some issues and ignoring others.

First, we might want to distinguish between the basic notion of a magnetic monopole, i.e. any particle with a "magnetic charge", and the specific realizations of magnetic monopoles that occur in grand unified theories. From a purely empirical and open-minded standpoint, the logical possibility of particles with magnetic charge deserves some consideration, all the more so because it would explain charge quantization.

Then we have the 't Hooft-Polyakov monopoles of grand unified theories. Obviously, if one already thinks that grand unification is unlikely, it is legitimate to regard this kind of monopole as unlikely too. Also, as an internal matter of grand unification theory, it is already widely supposed by GUT advocates that any primordial monopoles were spread out by inflation and may now be undetectably rare.

However, I disagree with the argument apparently being advanced in #7. The proposition seems to be that the theoretical uncertainty about how fermion-monopole scattering works, is evidence that it mathematically can't work, in which case monopoles would be logically ruled out, not just empirically disfavored.

This is very unlikely given the centrality of monopoles to advanced field theory these days. It's one thing to say that N=4 super-Yang-Mills theory (and similar constructs) have nothing to do with the physical world. But to say that fermion-monopole scattering cannot be made to work, seems to imply that all those "theories" don't even work as mathematics. And remember, those theories actually have applications in pure math - for example, you can characterize a manifold by how many solutions a given field theory has on that manifold.

(If I have misunderstood the meaning of #7, please explain!)

So my point is that whether or not the real world contains monopoles, this mystery regarding fermion-monopole scattering is going to have a mathematically correct answer, that will reveal more about the workings of the field theories in which it occurs.

Meanwhile, I want to return to something else I said in #5:

field configurations described as monopoles occur even in the gauge theories of the standard model

This is mentioned in a footnote on the first page of the paper in #3: "dynamical monopoles are typically present in lattice realizations of gauge theories". I am not clear enough on this to give my own description of how it works, but it is described e.g. in the first few pages of this 1992 preprint, where it's said that a nonabelian gauge field is capable of giving rise to these "dynamical monopoles" in a lattice description. Evidently they are some kind of topological object - comparable to a soliton or an instanton - that can arise in a path integral. And they are important enough that the condensation of dynamical monopoles in the gluon fields, has been proposed as the cause of confinement in QCD.

(At this point I can't say whether the "problem of fermion-monopole scattering" is an issue for this kind of monopole as well.)

Finally, I would like to say that the "problem of fermion-monopole scattering", whether or not it is only a mathematical problem, touches on topics other than monopoles, that are of physical interest. These are the higher symmetries and non-invertible symmetries that I mentioned, and also the "topological surfaces" mentioned in the abstract in #3. These new classes of symmetry have been found in the standard model! They are a new nuance of some field theories that are very definitely physical, and deserve to be understood.