Deconfinement transition for quarks on a line

We examine the statistical mechanics of a one-dimensional gas of both adjoint and fundamental representation quarks which interact with each other through (1 + 1)-dimensional U(N) gauge fields. Using large-N expansion we show that, when the density of fundamental quarks is small, there is a first-order phase transition al a critical temperature and adjoint quark density which can be interpreted as deconfinement. When the fundamental quark density is comparable to the adjoint quark density, the phase transition becomes a third order one. We formulate a way to distinguish the phases by considering the expectation values of high winding number Polyakov loop operators. (C) 1997 Academic Press.