Noncommutativities of D-branes and $\theta$-changing Degrees of Freedom in D-brane Matrix Models

TL;DR

This paper explores the origins of noncommutativity in D-brane world volumes, linking coordinate and momentum noncommutativities to the noncommutative Yang-Mills theory and showing how these can be transformed or fixed via coordinate changes.

Contribution

It demonstrates that the noncommutativity in D-brane world volumes arises from both transverse coordinates and momenta, and shows how it can be transformed through coordinate changes, connecting to Seiberg-Witten theory.

Findings

Noncommutativity of world volume coordinates originates from transverse coordinate and momentum noncommutativities.

Coordinate transformations can fix the noncommutativity to an arbitrary value.

Relation between noncommutativity and hidden symmetries in IIB matrix models.

Abstract

It is known that when there are several D-branes, their space-time coordinates in general become noncommutative. From the point of view of noncommutative geometry, it reflects noncommutativity of the world volume of the D-branes. On the other hand, as we showed in the previous work, in the presence of the constant antisymmetric tensor field the momentum operators of the D-branes have noncommutative structure. In the present paper, we investigate a relation between these noncommutativities and the description of D-branes in terms of the noncommutative Yang-Mills theory recently proposed by Seiberg and Witten. It is shown that the noncommutativity of the Yang-Mills theory, which implies that of the world volume coordinates, originates from both noncommutativities of the transverse coordinates and momenta from the viewpoint of the lower-dimensional D-branes. Moreover, we show that this noncommutativity is transformed by coordinate transformations on the world volume and thereby can be chosen in an arbitrary fixed value. We also make a brief comment on a relation between this fact and a hidden symmetry of the IIB matrix models.