A Bottom-Up EFT Approach To Superdense Baryonic Matter

How to arrive at the densest matter in massive compact stars starting from Walecka's linear $\omega$-$\sigma$ mean-field model is described in a series of arguments anchored on hidden local symmetry, hidden scale symmetry and emergent parity-doublet symmetry. I follow the bottom-up approach from chiral symmetry with pions, coupled to hidden local and scale symmetry degrees of freedom. Exploiting the renormalization-group treatment \`a la Shankar and Polchinski of the fermionic interactions on the Fermi sphere, leading to Landau-Migdal Fermi-liquid, one obtains a sort of generalized ``Density Functional" that allows via a topology change hadrons transform to quarks without phase changes at the center of massive stars. The highly dense matter is ``pseudo-conformal" with the sound velocity $v_{pcs}^2/c^2\approx 1/3$ but the trace of the energy-momentum tensor is not equal to zero, hence the matter is non-conformal.