New model of high-spin Baryons

[mitchell porter]

They are described here as (2+1)-dimensional sheets of eta-prime condensate, with the valence quarks on the boundary. One amazing detail is that, because it is a lower-dimensional object, the quarks are anyons!

This description is said to apply most immediately to single-flavor baryons like ∆++ and Ω−.

https://arxiv.org/abs/1812.09253
Baryons as Quantum Hall Droplets
Zohar Komargodski
(Submitted on 21 Dec 2018)
We revisit the problem of baryons in the large N limit of Quantum Chromodynamics. A special case in which the theory of Skyrmions is inapplicable is one-flavor QCD, where there are no light pions to construct the baryon from. More generally, the description of baryons made out of predominantly one flavor within the Skyrmion model is unsatisfactory. We propose a model for such baryons, where the baryons are interpreted as quantum Hall droplets. An important element in our construction is an extended, 2+1 dimensional, meta-stable configuration of the η′ particle. Baryon number is identified with a magnetic symmetry on the 2+1 dimensional sheet. If the sheet has a boundary, there are finite energy chiral excitations which carry baryon number. These chiral excitations are analogous to the electron in the fractional quantum Hall effect. Studying the chiral vertex operators we are able to determine the spin, isospin, and certain excitations of the droplet. In addition, balancing the tension of the droplet against the energy stored at the boundary we estimate the size and mass of the baryons. The mass, size, spin, isospin, and excitations that we find agree with phenomenological expectations.

 

[mitchell porter]

In April, Komargodski gave a talk about this ongoing work (video, slides). He says (video, 36m50s fwd) that sheets of eta-prime condensate have been discussed before, in the context of high density and high "chemical potential", e.g. inside neutron stars, but "people have completely missed the fact that there is a Chern-Simons field theory on these sheets, and instead there were some roundabout arguments with anomaly inflow, about some excitations on the boundaries of these sheets".

This week, representatives of the "anomaly inflow" school of thought (Mannque Rho and collaborators) have posted their version of this idea, "Baryon as a Quantum Hall Droplet and the Cheshire Cat Principle". I don't quite get the Cheshire Cat principle - something to do with the idea that a bag model of hadrons should give the same predictions, even if the bag is shrunk to a point - but Rho has coauthored many papers about it; here is one from 1992 about the eta-prime.

Komargodski also says (video, 26m30s fwd; slide 29 of his talk) that his concept can be realized within holographic QCD. The work he mentions is already cited in his 2018 paper (footnote 26) as in progress, and it's still in progress.

There are many many details to absorb here, but I'll mention one simple detail that I only picked up this time: the sheets are a mixture of eta-prime meson and glueballs. The sheet is supposed to interpolate between two phases of QCD with different densities of instantons, and this has something to do with the glueball component.

 

[mitchell porter]

"Skyrmions, Quantum Hall Droplets, and one current to rule them all" by Avner Karasik obtains this unusual Nf=1 (one-flavor) model, as a limit of a more conventional Nf=2 skyrmion model, in which one flavor becomes heavy. The key technical development is in equation 4.9, a new current H which amends the usual skyrmion current B.

 

[mitchell porter]

"Hall Droplet Sheets in Holographic QCD" realizes this concept of one-flavor baryons as sheets of eta-prime condensate, in the QCD-like context of a well-known string theory construction.