Lectures on Effective Field Theories for Nuclei, Nuclear Matter and Dense Matter

TL;DR

This paper explores the connection between old and modern notions of quark-baryon dualities in nuclear matter, predicting meson behavior at high densities relevant to compact stars, using concepts like color-flavor locking and hidden gauge symmetry.

Contribution

It introduces novel ideas linking Cheshire Cat principles, quark-baryon dualities, and meson behavior in dense matter, emphasizing potential experimental confirmations.

Findings

Vector mesons as Higgsed gluons in dense matter

Equivalence of hidden flavor gauge and color gauge symmetries

Predictions for meson behavior in high-density nuclear environments

Abstract

This note is based on four lectures that I gave at the 10th Taiwan Nuclear Spring School held at Hualien, Taiwan in January 2002. It aims to correlate the old notion of Cheshire Cat Principle developed for elementary baryons to the modern notion of quark-baryon and gluon-meson "continuities" or "dualities" in dilute and dense many-body systems and predict what would happen to mesons when squeezed by nuclear matter to high density as possibly realized in compact stars. Using color-flavor locking in QCD, the vector mesons observed at low density can be described as the Higgsed gluons dressed by cloud of collective modes, i.e., pions just as they are in superdense matter, thus showing the equivalence between hidden $flavor$ gauge symmetry and explicit $color$ gauge symmetry. Instead of going into details of well-established facts, I focus on a variety of novel ideas -- some solid and some less -- that could be confirmed or ruled out in the near future.