Baryons as Quantum Hall Droplets

Abstract

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 ${\eta }^{\prime }$ 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.

27 pages, 2 figures. v2: references and some clarifications added

References in corpus (5)

• Generalized Global Symmetries
• Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d
• Three-dimensional dualities with bosons and fermions
• Skyrmions and clustering in light nuclei
• QCD domain walls, Chern-Simons theories and holography

Cited by in corpus (13)

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• Skyrmions, Quantum Hall Droplets, and one current to rule them all
• From 3d dualities to hadron physics
• Deconfinement on axion domain walls
• Vector dominance, one flavored baryons, and QCD domain walls from the "hidden" Wess-Zumino term
• Anomalies for anomalous symmetries
• Dichotomy of Baryons as Quantum Hall Droplets and Skyrmions In Compact-Star Matter
• A consistent two-skyrmion configuration space from instantons
• Fractionalized Quasiparticles in Dense Baryonic Matter
• Mapping topology to nuclear dilaton-HLS effective field theory for dense baryonic matter
• Tensor supercurrent in QCD
• Flavored extended instanton in QCD
• The "Folk Theorem" on Effective Field Theory: A Case for Nuclear Physics