# Baryonic or quarkyonic matter?

## TL;DR

This paper reviews an effective theory for cold, dense QCD with heavy quarks, analyzing the $N_c$-dependence of phase transitions and the equation of state, suggesting baryonic and quarkyonic matter may be equivalent at nuclear densities.

## Contribution

It introduces and studies a 3d effective theory for dense QCD, exploring the $N_c$-dependence of phase transitions and the scaling of pressure, proposing a potential equivalence of baryonic and quarkyonic matter.

## Key findings

- Transition becomes more first order with increasing $N_c$.
- Critical endpoint moves to high temperatures at large $N_c$.
- Pressure scales as $p o N_c$, indicating possible equivalence of baryonic and quarkyonic matter.

## Abstract

During the last years it has become possible to address the cold and dense regime of QCD directly for sufficiently heavy quarks, where combined strong coupling and hopping expansions are convergent and a 3d effective theory can be derived, which allows to control the sign problem either in simulations or by fully analytic calculations. In this contribution we review the effective theory and study the $N_c$-dependence of the nuclear liquid gas transition, as well as the equation of state of baryonic matter in the strong coupling limit. We find the transition to become more strongly first order with growing $N_c$, suggesting that in the large $N_c$ limit its critical endpoint moves to high temperatures to connect with the deconfinement transition. Furthermore, to leading and next-to-leading order in the strong coupling and hopping expansions, respectively, the pressure is found to scale as $p\sim N_c$. This suggests that baryonic and quarkyonic matter might be the same at nuclear densities. Further work is needed to see whether this result is stable under gauge corrections.