FINITE-TEMPERATURE LATTICE QCD IN THE LARGE N LIMIT

Our aim is to give a self-contained review of recent advances in the a nalytic description of the deconfinement transition and determination of the deconfinement temperature in lattice QCD at large N. We also in clude some new results, as for instance in the comparison of the analy tic results with Monte Carlo simulations. We first review the general set-up of finite temperature lattice gauge theories, using asymmetric lattices, and develop a consistent perturbative expansion in the coupl ing beta(s) of the spacelike plaquettes. We study in detail the effect ive models for the Polyakov loop obtained, in the zeroth order approxi mation in beta(s),, both from the Wilson action (symmetric lattice) an d from the heat kernel action (completely asymmetric lattice). The dis tinctive feature of the heat kernel model is its relation with two-dim ensional QCD on a cylinder; the Wilson model, on the other hand, can b e exactly reduced to a twisted one-plaquette model via a procedure of the Eguchi-Kawai type. In the weak coupling regime both models can be related to exactly solvable Kazakov-Migdal matrix models. The instabil ity of the weak coupling solution is due in both cases to a condensati on of instantons; in the heat kernel case, this is directly related to the Douglas-Kazakov transition of QCD2. A detailed analysis of these results provides rather accurate predictions of the deconfinement temp erature. In spite of the zeroth order approximation they are in good a greement with the Monte Carlo simulations in 2 + 1 dimensions, while i n 3 + 1 dimensions they only agree with the Monte Carlo results away f rom the continuum limit.