# QCD in the heavy dense regime for general $N_c$: On the existence of quarkyonic matter

## TL;DR

This paper investigates the phase transition to quarkyonic matter in lattice QCD with heavy quarks, showing that the transition becomes stronger with larger N_c and that the pressure scales as N_c in the baryon condensed regime, indicating a distinct phase.

## Contribution

It provides a detailed analysis of the cold, dense regime of lattice QCD for general N_c, demonstrating the emergence of quarkyonic matter and its properties through series expansion methods.

## Key findings

- Transition to baryon condensation becomes first-order at large N_c.
- Pressure in the baryon condensed phase scales as N_c.
- Identifies a phase with mixed baryon and quark characteristics, termed quarkyonic.

## Abstract

Lattice QCD with heavy quarks reduces to a three-dimensional effective theory of Polyakov loops, which is amenable to series expansion methods. We analyse the effective theory in the cold and dense regime for a general number of colours, $N_c$. In particular, we investigate the transition from a hadron gas to baryon condensation. For any finite lattice spacing, we find the transition to become stronger, i.e. ultimately first-order, as $N_c$ is made large. Moreover, in the baryon condensed regime, we find the pressure to scale as $p\sim N_c$ through three orders in the hopping expansion. Such a phase differs from a hadron gas with $p\sim N_c^0$, or a quark gluon plasma, $p\sim N_c^2$, and was termed quarkyonic in the literature, since it shows both baryon-like and quark-like aspects. A lattice filling with baryon number shows a rapid and smooth transition from condensing baryons to a crystal of saturated quark matter, due to the Pauli principle, and is consistent with this picture. For continuum physics, the continuum limit needs to be taken before the large $N_c$ limit, which is not yet possible in practice. However, in the controlled range of lattice spacings and $N_c$-values, our results are stable when the limits are approached in this order. We discuss possible implications for physical QCD.