Morita Duality and Noncommutative Wilson Loops in Two Dimensions

Abstract

We describe a combinatorial approach to the analysis of the shape and orientation dependence of Wilson loop observables on two-dimensional noncommutative tori. Morita equivalence is used to map the computation of loop correlators onto the combinatorics of non-planar graphs. Several nonperturbative examples of symmetry breaking under area-preserving diffeomorphisms are thereby presented. Analytic expressions for correlators of Wilson loops with infinite winding number are also derived and shown to agree with results from ordinary Yang-Mills theory.

32 pages, 9 figures; v2: clarifying comments added; Final version to be published in JHEP

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• Toy models for wrapping effects
• Probability distribution of the index in gauge theory on 2d non-commutative geometry
• Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 2. 1/θExpansion
• Gauge-Invariant Resummation Formalism and Unitarity in Non-Commutative QED
• Area-preserving diffeomorphisms in gauge theory on a non-commutative plane: a lattice study
• Wilson Loops and Area-Preserving Diffeomorphisms in Twisted Noncommutative Gauge Theory
• Area preserving diffeomorphisms and Yang-Mills theory in two noncommutative dimensions