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.
Highlights
Our approach is anchored on two symmetries hidden in dilute hadronic systems, i.e., chiral symmetry and scale symmetry, that could play a crucial role as density increases high
One of our basic assumptions is that the hidden local symmetry (HLS) is consistent with the Suzuki theorem [10], and the scale symmetry with genuine dilaton has an infrared (IR) fixed point with both the chiral and scale symmetries realized in the NG mode [11] at some high density
We find that the combined hidden scale symmetry (HSS) and HLS, suitably formulated so as to access high density compact-star matter [8], not necessarily intrinsic in QCD but interpreted as “emergent” from strong nuclear correlations, reveals a dichotomy in the structure of baryons treated in terms of topology in the large Nc approximation and discuss how it could affect the equation of state (EoS) at high density relevant to the cores of massive compact stars
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. One of our basic assumptions is that the HLS is consistent with the Suzuki theorem [10], and the scale symmetry with genuine dilaton has an infrared (IR) fixed point with both the chiral and scale symmetries realized in the NG mode [11] at some high density How these symmetries, invisible in free space, could appear in dense medium has been the subject of the past efforts [8] in nuclear astrophysics and motivates us to go beyond what has been explored so far. We find that the combined hidden scale symmetry (HSS) and HLS, suitably formulated so as to access high density compact-star matter [8], not necessarily intrinsic in QCD but interpreted as “emergent” from strong nuclear correlations, reveals a dichotomy in the structure of baryons treated in terms of topology in the large Nc approximation and discuss how it could affect the equation of state (EoS) at high density relevant to the cores of massive compact stars. The merit of this work is that it exploits in strongly interacting baryonic matter a certain ubiquitous topological structure of highly correlated fermions, similar to electrons in condensed matter, thereby bringing in a possible paradigm change in nuclear dynamics
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