TL;DR
This paper explores how topologically nontrivial gauge transformations in noncommutative gauge theories relate to their commutative equivalents through the Seiberg-Witten map, clarifying their topological and action correspondence.
Contribution
It analyzes the gauge transformation component of the Seiberg-Witten map and clarifies the relation of Chern-Simons actions between noncommutative and commutative theories.
Findings
The gauge transformation part of the Seiberg-Witten map is characterized.
Chern-Simons actions in noncommutative and commutative theories are explicitly related.
The topological aspects of gauge transformations are elucidated.
Abstract
The mapping of topologically nontrivial gauge transformations in noncommutative gauge theory to corresponding commutative ones is investigated via the operator form of the Seiberg-Witten map. The role of the gauge transformation part of the map is analyzed. Chern-Simons actions are examined and the correspondence to their commutative counterparts is clarified.
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