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We take a first step towards the solution of QCD in 1+1 dimensions at nonzerodensity. We regularize the theory in the UV by using a lattice and in the IR byputting the theory in a box of spatial size L. After fixing to axial gauge weuse the coherent states approach to obtain the large-N classical Hamiltonian Hthat describes color neutral quark-antiquark pairs interacting with spatialPolyakov loops in the background of baryons. Minimizing H we get a regularizedform of the `t Hooft equation that depends on the expectation values of thePolyakov loops. Analyzing the L-dependence of this equation we show how volumeindependence, a la Eguchi and Kawai, emerges in the large-N limit, and how itdepends on the expectation values of the Polyakov loops. We describe how thisindependence relies on the realization of translation symmetry, in particularwhen the ground state contains a baryon crystal. Finally, we remark on theimplications of our results on studying baryon density in large-N QCD withinsingle-site lattice theories, and on some general lessons concerning the wayfour-dimensional large-N QCD behaves in the presence of baryons.

Volume dependence of two-dimensional large-N QCD with a nonzero density of baryons