Dichotomy of Baryons as Quantum Hall Droplets and Skyrmions: Topological Structure of Dense Matter

Abstract

We review a new development on the possible direct connection between the topological structure of the Nf=1 baryon as a FQH droplet and that of the Nf≥2 baryons (such as nucleons and hyperons) as skyrmions. This development suggests a possible “domain-wall (DW)” structure of compressed baryonic matter at high density expected to be found in the core of massive compact stars. Our theoretical framework is anchored on an effective nuclear effective field theory that incorporates two symmetries either hidden in the vacuum in QCD or emergent from strong nuclear correlations. It presents a basically different, hitherto undiscovered structure of nuclear matter at low as well as high densities. Hidden “genuine dilaton (GD)” symmetry and hidden local symmetry (HLS) gauge-equivalent at low density to nonlinear sigma model capturing chiral symmetry, put together in nuclear effective field theory, are seen to play an increasingly important role in providing hadron–quark duality in baryonic matter. It is argued that the FQH droplets could actually figure essentially in the properties of the vector mesons endowed with HLS near chiral restoration. This strongly motivates incorporating both symmetries in formulating “first-principles” approaches to nuclear dynamics encompassing from the nuclear matter density to the highest density stable in the Universe.

Mapping Topology of Skyrmions and Fractional Quantum Hall Droplets to Nuclear EFT for Ultra-Dense Baryonic Matter

“…As argued in [63], the FQH droplet should become relevant at some high density at which f χ → 0. This density must then be (much) higher than that reached at the DLFP close to the GD's IR fixed point.…”

“…There are two questions raised regarding this dichotomy [63] between the skyrmions and the FQH droplets. The first is: is there any relation between the two topological objects, the FQH droplet for B (0) and the skyrmion for nucleons?…”

“…The notable observation made by Karasik [31,52] is that what is called "hidden" Wess-Zumino term in the HLS Lagrangian (replacing the "homogeneous" Wess-Zumino term of [13]) unifies the baryon currents for both the FQH droplet and the skyrmions [63]. It was noted that in the effective field theory that contains both η and the HLS fields, the η cusp that accounts for the jump from one vacuum to the other at η = π does not appear.…”

Scale symmetry and composition of compact star matter

“…Dense nuclear matter relevant to the core of compact star is an uncharted domain although it has been studied for several decades [1][2][3][4][5][6][7][8]. Several fundamental but significant questions in dense nuclear matter, such as the pattern of symmetry, the constituents and so on are not yet well understood.…”

“…Several fundamental but significant questions in dense nuclear matter, such as the pattern of symmetry, the constituents and so on are not yet well understood. The recent observations of massive neutron stars with about two times solar mass and detections of the gravitational waves from binary neutron star mergers and neutron star-black hole mergers open new laboratories for dense nuclear matter (see, e.g., [5][6][7][8] and references therein).…”