On the short-distance structure of irrational non-commutative gauge theories

Abstract

As shown by Hashimoto and Itzhaki in hep-th/9911057, the perturbative degrees of freedom of a non-commutative Yang-Mills theory (NCYM) on a torus are quasi-local only in a finite energy range. Outside that range one may resort to a Morita equivalent (or T-dual) description appropriate for that energy. In this note, we study NCYM on a non-commutative torus with an irrational deformation parameter $\theta$. In that case, an infinite tower of dual descriptions is generically needed in order to describe the UV regime. We construct a hierarchy of dual descriptions in terms of the continued fraction approximations of $\theta$. We encounter different descriptions depending on the level of the irrationality of $\theta$ and the amount of non-locality tolerated. The behavior turns out to be isomorphic to that found for the phase structure of the four-dimensional Villain $Z_N$ lattice gauge theories, which we revisit as a warm-up. At large 't Hooft coupling, using the AdS/CFT correspondance, we find that there are domains of the radial coordinate $U$ where no T-dual description makes the derivative expansion converge. The radial direction obtains multifractal characteristics near the boundary of AdS.

17 pages, 4 figures, uses JHEP.cls

References in corpus (5)

• Large N Limit of Non-Commutative Gauge Theories
• Magnetic fields, branes and noncommutative geometry
• OM Theory in Diverse Dimensions
• 1/4-BPS states on noncommutative tori
• Supergravity and "New" Six-Dimensional Gauge Theories

Cited by in corpus (9)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Morita Duality and Large-N Limits
• Aspects of Gauge Theory on Commutative and Noncommutative Tori
• The BRS invariance of noncommutative U(N) Yang-Mills theory at the one-loop level
• Melvin Models and Diophantine Approximation
• The spectrum of 2+1 dimensional Yang-Mills theory on a twisted spatial torus
• Les Houches lectures on supersymmetric Gauge Theories
• Instantons, Fluxons and Open Gauge String Theory