QCD\
with a nonzero density of baryons.** ]{}

Introduction
============

QCD simplifies in the ’t Hooft limit of a large number of colors, and as a result it has been a long-standing goal to understand the properties of the theory in that limit [@largeN], including on the lattice [@lattice-reviews]. One alternative to conventional large volume simulations is the use the large-$N$ equivalence of QCD at large volume to QCD with zero volume [@EK; @BHN1; @MK; @Migdal; @TEK; @AEK; @DW; @GK; @Parisipapers] (see also the related Ref. [@KNN]). These large-$N$ volume reductions allows one, in principle, to study very large values of $N\sim
O(100-400)$ with modest resources.

Volume reduction holds only if the ground states of the large and zero volume theories respect certain symmetries [@AEK]. Unfortunately, in the most interesting case of QCD in four dimensions these symmetries spontaneously break in the continuum limit when a naive reduction prescription is used [@BHN1; @MK]. An extension of that prescription is thus required and for a recent summary of the literature on this topic we refer to the reviews in the recent Refs. [@QEK; @DEK].

In the case of two space-time dimensions – the ‘t Hooft model – a naive large-$N$ volume 