Classical Solutions of the TEK Model and Noncommutative Instantons in Two Dimensions

The twisted Eguchi-Kawai (TEK) model provides a non-perturbative definitionof noncommutative Yang-Mills theory: the continuum limit is approached at large$N$ by performing suitable double scaling limits, in which non-planarcontributions are no longer suppressed. We consider here the two-dimensionalcase, trying to recover within this framework the exact results recentlyobtained by means of Morita equivalence. We present a rather explicitconstruction of classical gauge theories on noncommutative toroidal lattice forgeneral topological charges. After discussing the limiting procedures torecover the theory on the noncommutative torus and on the noncommutative plane,we focus our attention on the classical solutions of the related TEK models. Wesolve the equations of motion and we find the configurations having finiteaction in the relevant double scaling limits. They can be explicitly describedin terms of twist-eaters and they exactly correspond to the instanton solutionsthat are seen to dominate the partition function on the noncommutative torus.Fluxons on the noncommutative plane are recovered as well. We also discuss howthe highly non-trivial structure of the exact partition function can emergefrom a direct matrix model computation. The quantum consistency of the TEKformulation is eventually checked by computing Wilson loops in a particularlimit.Comment: 41 pages, JHEP3. Minor corrections, references adde