Wilson lines on noncommutative tori
Anton Alekseev, Andrei Bytsko
TL;DR
This paper introduces noncommutative Wilson lines on tori, showing their invariance under the Seiberg-Witten map, thus extending gauge theory concepts to noncommutative geometry.
Contribution
It defines noncommutative Wilson lines via monodromy for gauge fields with zero curvature, demonstrating their invariance under the Seiberg-Witten map.
Findings
Wilson lines are well-defined on noncommutative tori
Wilson lines remain invariant under Seiberg-Witten map
Extends gauge theory concepts to noncommutative geometry
Abstract
We introduce the notion of a monodromy for gauge fields with vanishing curvature on the noncommutative torus. Similar to the ordinary gauge theory, traces of the monodromies define noncommutative Wilson lines. Our main result is that these Wilson lines are invariant under the Seiberg-Witten map changing the deformation parameter of the noncommutative torus.
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