The Smile of Cheshire Cat At High Density

TL;DR

This paper explores a theoretical framework linking baryonic matter in dense environments to quantum Hall states and dilaton limits, proposing a new structure of matter at high density with implications for neutron stars.

Contribution

It introduces a novel conceptual link between baryonic matter and quantum Hall droplets at high density using the Cheshire Cat Principle in QCD.

Findings

High-density baryonic matter may form quantum Hall-like structures.

The dilaton-limit fixed point is approached at high density, with specific decay constants.

The scenario allows for possible phase transitions in neutron star cores.

Abstract

Baryons in finite nuclei, nuclear matter and dense compact-star matter are described in terms of Cheshire Cat for QCD. A potential conceptual link, admittedly short in mathematical rigor, between their manifestations is made by what's called Cheshire Cat Principle. Put in terms taken ``dual" to QCD variables, going to very high density exposes quantum Hall droplets -- or pancakes -- at which the dilaton-limit fixed point with $g_A\to 1$, $f_\pi\to f_\chi$ -- where $f_\pi$ and $f_\chi$ are respectively the pion and dilaton decay constants -- and the baryon parity-doubling are reached. This scenario suggests a thus-far totally unexplored structure of dual baryonic matter at high density which does neither require nor rule out (rapid) first-order phase transitions from hadrons to quarks in the core of compact stars on the verge of gravitational collapse.