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Skyrmions, Quantum Hall Droplets, and one current to rule them all

by Avner Karasik

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Submission summary

Authors (as registered SciPost users): Avner Karasik
Submission information
Preprint Link:  (pdf)
Date submitted: 2020-04-02 02:00
Submitted by: Karasik, Avner
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


We introduce a novel Skyrme-like conserved current in the effective theory of pions and vector mesons based on the idea of hidden local symmetry. The associated charge is equivalent to the skyrmion charge for any smooth configuration. In addition, there exist singular configurations that can be identified as N_f=1 baryons charged under the new symmetry. Under this identification, the vector mesons play the role of the Chern-Simons vector fields living on the quantum Hall droplet that forms the N_f=1 baryon. We propose that this current is the correct effective expression for the baryon current at low energies. This proposal gives a unified picture for the two types of baryons and allows them to continuously transform one to the other in a natural way. In addition, Chern-Simons dualities on the droplet can be interpreted as a result of Seiberg-like duality between gluons and vector mesons.

Current status:
Has been resubmitted

Reports on this Submission

Anonymous Report 1 on 2020-4-7 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2003.07893v2, delivered 2020-04-07, doi: 10.21468/SciPost.Report.1612


1) The paper nicely summarizes the existing constructions to describe baryons in terms of low energy descriptions in the literature.

2) The paper gives a nice unifying description that works for the two seemingly completely disconnected existing ideas for one flavor and two or more flavors.

3) The paper performs many checks to confirm the picture is correct.


1) The paper is presumably the final word on the story, closing a loophole in our understanding of baryons as skyrmions. While it is very nice work, it is unlikely to stimulate large amounts of follow up work or open new doors.


The low energy degrees of freedom of QCD are the pions, the Goldstone bosons of broken chiral symmetry. The correct low energy description of QCD is a theory of pions. Baryons in this language arise as non-perturbative objects made out of pions. At least this is the well established story for 2 or more flavors. For 1 flavor, the global symmetry is only U(1) baryon number to begin with and so there is no chiral symmetry breaking and hence no pions, so the story appears very different. At large N, a second U(1) appears, the otherwise anomalous axial U(1) whose anomaly is suppressed at large N, and so a new light boson appears as well, the eta'. It has been argued in previous work that in this case the baryon again can be written as some exotic soliton like excitation.

These two descriptions for the baryon both appeared individually correct, but are conceptually completely disconnected. This is puzzling, as the standard skyrmion for 2 or more flavors should go over to the new soliton in the limit that one makes all but one flavor very heavy. This is the problem solved in this paper. A unifying description is given, based on the hidden symmetry approach to QCD, that smoothly interpolates between the standard skyrmion description for 2 or more flavors and the novel soliton for 1 flavor.

  • validity: high
  • significance: good
  • originality: high
  • clarity: top
  • formatting: perfect
  • grammar: excellent

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