2003/11/19 by Luca Griguolo, Domenico Seminara · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #hep-th
paper · pdf · doi:10.1088/1126-6708/2004/03/068
published as JHEP 0403 (2004) 068 · 41 pages, JHEP3. Minor corrections, references added
arxiv created 2003/11/19 · openalex publication_date 2004/03/30 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The twisted Eguchi-Kawai (TEK) model provides a non-perturbative definition of noncommutative Yang-Mills theory: the continuum limit is approached at large N by performing suitable double scaling limits, in which non-planar contributions are no longer suppressed. We consider here the two-dimensional case, trying to recover within this framework the exact results recently obtained by means of Morita equivalence. We present a rather explicit construction of classical gauge theories on noncommutative toroidal lattice for general topological charges. After discussing the limiting procedures to recover the theory on the noncommutative torus and on the noncommutative plane, we focus our attention on the classical solutions of the related TEK models. We solve the equations of motion and we find the configurations having finite action in the relevant double scaling limits. They can be explicitly described in terms of twist-eaters and they exactly correspond to the instanton solutions that are seen to dominate the partition function on the noncommutative torus. Fluxons on the noncommutative plane are recovered as well. We also discuss how the highly non-trivial structure of the exact partition function can emerge from a direct matrix model computation. The quantum consistency of the TEK formulation is eventually checked by computing Wilson loops in a particular limit.