Pseudoconformal equation of state in compact-star matter from topology change and hidden symmetries of QCD

Abstract

We construct a new effective field theory approach to the equation of state (EoS), dubbed pseudo-confomal model “PCM, for nuclear and compact star matter entirely in terms of effective hadron degrees of freedom. The possible transition at $n\!\sim$(2-4)$n_0$ (where $n_0$ is the normal nuclear matter density) from hadron degrees of freedom to strongly-coupled quark degrees of freedom, giving rise to a soft-to-hard changeover in the EoS that can accommodate the massive stars observed, is effectuated by the topology change at $n_{1/2}\mathrel{\rlap{\lower3pt\hbox{\hskip1pt$∼$}}\raise1pt\hbox{$>$}}2n_0$ from skyrmions to half-skyrmions without involving local order-parameter fields. The mechanism exploits possible emergence of hidden scale and local symmetries of QCD at high density, leading to a precocious “pseudo-conformal sound velocity $v_{\rm~s}^2=1/3$ (in unit of $c=1$) for $n\mathrel{\rlap{\lower3pt\hbox{\hskip1pt$∼$}}\raise1pt\hbox{$>$}}3n_0$. The resulting prediction signals a drastic departure from standard nuclear many-body theory in the density regime involved in the massive stars. We suggest that the tidal deformability implemented in gravitational waves coming from coalescing neutron stars in LIGO/Virgo-type observations could pin down the location of the topology change density $n_{1/2}$.