Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-09-21
Nucl.Phys. B623 (2002) 165-200
Physics
High Energy Physics
High Energy Physics - Theory
41 pages, Harvmac. Some corrections to section 6.3. Comments added on Hall Effect
Scientific paper
10.1016/S0550-3213(01)00624-1
We study some dynamical aspects of gauge theories on noncommutative tori. We show that Morita duality, combined with the hypothesis of analyticity as a function of the noncommutativity parameter Theta, gives information about singular large-N limits of ordinary U(N) gauge theories, where the large-rank limit is correlated with the shrinking of a two-torus to zero size. We study some non-perturbative tests of the smoothness hypothesis with respect to Theta in theories with and without supersymmetry. In the supersymmetric case this is done by adapting Witten's index to the present situation, and in the nonsupersymmetric case by studying the dependence of energy levels on the instanton angle. We find that regularizations which restore supersymmetry at high energies seem to preserve Theta-smoothness whereas nonsupersymmetric asymptotically free theories seem to violate it. As a final application we use Morita duality to study a recent proposal of Susskind to use a noncommutative Chern-Simons gauge theory as an effective description of the Fractional Hall Effect. In particular we obtain an elegant derivation of Wen's topological order.
Alvarez-Gaume Luis
Barbon Jose L. F.
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