Comments on Gauge Equivalence in Noncommutative Geometry

TL;DR

This paper examines the gauge transformation ambiguity in noncommutative geometry, revealing its path dependence in theta-space and implications for gauge equivalence, especially in non-Abelian cases.

Contribution

It clarifies the nature of gauge transformation ambiguities in noncommutative gauge theories and their relation to field redefinitions, extending previous work by Seiberg and Witten.

Findings

Path dependence of gauge transformations in theta-space.

Ambiguity negligible in U(1) with slowly varying fields.

Non-negligible ambiguity in U(N) and higher derivative cases.

Abstract

We investigate the transformation from ordinary gauge field to noncommutative one which was introduced by N.Seiberg and E.Witten (hep-th/9908142). It is shown that the general transformation which is determined only by gauge equivalence has a path dependence in `\theta-space'. This ambiguity is negligible when we compare the ordinary Dirac-Born-Infeld action with the noncommutative one in the U(1) case, because of the U(1) nature and slowly varying field approximation. However, in general, in the higher derivative approximation or in the U(N) case, the ambiguity cannot be neglected due to its noncommutative structure. This ambiguity corresponds to the degrees of freedom of field redefinition.