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abstract: 'We take a first step towards the solution of QCD in $1+1$ dimensions at nonzero density. We regularize the theory in the UV by using a lattice and in the IR by putting the theory in a box of spatial size $L$. After fixing to axial gauge we use the coherent states approach to obtain the large-$N$ classical Hamiltonian ${\cal H}$ that describes color neutral quark-antiquark pairs interacting with spatial Polyakov loops in the background of baryons. Minimizing ${\cal H}$ we get a regularized form of the ‘t Hooft equation that depends on the expectation values of the Polyakov loops. Analyzing the $L$-dependence of this equation we show how volume independence, à la Eguchi and Kawai, emerges in the large-$N$ limit, and how it depends on the expectation values of the Polyakov loops. We describe how this independence relies on the realization of translation symmetry, in particular when the ground state contains a baryon crystal. Finally, we remark on the implications of our results on studying baryon density in large-$N$ QCD within single-site lattice theories, and on some general lessons concerning the way four-dimensional large-$N$ QCD behaves in the presence of baryons.'
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[**Volume dependence of two-dimensional large-$N$ 