QCD in the heavy dense regime for general Nc: on the existence of quarkyonic matter

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 ∼ N c through three orders in the hopping expansion. Such a phase differs from a hadron gas with p ∼ N 0 c , or a quark gluon plasma, p ∼ N 2 c , 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.

Heavy holographic QCD

“…1 of Ref. [10]. The similarity becomes even more striking when we go to our intermediate regime where there is a low-temperature discontinuous transition with a critical endpoint.…”

“…1 of Ref. [10]. Secondly, heavy QCD becomes pure Yang-Mills in the limit of infinitely heavy quarks.…”

“…It is tempting to compare our results to lattice QCD, where at large quark masses and large coupling the phase structure can be computed even for nonzero chemical potentials [10,32]. If we take our heaviest case and ignore the fact that our continuous phase transitions have higher-order discontinuities, the phase diagram has a intriguing similarity to the heavy QCD diagram, see for instance Fig.…”

“…For example, we shall compute the speed of sound for nonzero temperatures and chemical potentials, which also has been done in that approach [31]. Last but not least, we shall compare our results to recent calculations of QCD on the lattice, where a combined expansion for large coupling and large quark masses is used to circumvent the sign problem and thus is able to provide results for large baryon chemical potentials [10,32].…”

“…In its original form, the model is dual to QCD at a large number of colors N c (at least in a certain limit, which however is inaccessible with current methods). This is borne out in its phase structure [8], which can be mapped to large-N c QCD predictions [9,10]. Approaching the realistic regime of small N c in a rigorous way is very difficult, although N f /N c corrections, where N f is the number of flavors, have been discussed [11,12].…”