Singularities of the Seiberg-Witten map

Abstract

We construct an explicit solution of the Seiberg-Witten map for a linear gauge field on the non-commutative plane. We observe that this solution as well as the solution for a constant curvature diverge when the non-commutativity parameter theta reaches certain event horizon in the theta-space. This implies that an ordinary Yang-Mills theory can be continuously deformed by the Seiberg-Witten map into a non-commutative theory only within one connected component of the theta-space.

8 pages, LaTeX

Cited by in corpus (5)

• Magnetic fields in noncommutative quantum mechanics
• The Gauge Anomaly and the Seiberg-Witten Map
• Ambiguities of the Seiberg-Witten map in the presence of matter field
• Gauge Invariance and Noncommutativity
• Seiberg-Witten map and topology