Open Wilson Lines and Group Theory of Noncommutative Yang-Mills Theory in Two Dimensions

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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37 pages. References added

Scientific paper

10.1088/1126-6708/2003/05/029

The correlation functions of open Wilson line operators in two-dimensional Yang-Mills theory on the noncommutative torus are computed exactly. The correlators are expressed in two equivalent forms. An instanton expansion involves only topological numbers of Heisenberg modules and enables extraction of the weak-coupling limit of the gauge theory. A dual algebraic expansion involves only group theoretic quantities, winding numbers and translational zero modes, and enables analysis of the strong-coupling limit of the gauge theory and the high-momentum behaviour of open Wilson lines. The dual expressions can be interpreted physically as exact sums over contributions from virtual electric dipole quanta.

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