On open string σ-model and noncommutative gauge fields

We consider the ordinary and noncommutative Dirac-Born-Infeld theories within the open string σ-model. First, we propose a renormalization scheme, hybrid point splitting regularization, that leads directly to the Seiberg-Witten description including the two-form Φ. We also show how such a form appears within the standard renormalization scheme just by some freedom in changing variables. Second, we propose a Wilson factor which has the noncommutative gauge invariance on the classical level and then compute the σ-model partition function within one of the known renormalization scheme that preserves the noncommutative gauge invariance. As a result, we find the noncommutative Yang-Mills action.