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

Details Noncommutativities of D-branes and $θ$-changing Degrees of Freedom in D-brane Matrix Models Noncommutativities of D-branes and $θ$-changing Degrees of Freedom in D-brane Matrix Models

2000-01-04

arxiv.org/abs/hep-th/0001011v3

Phys.Lett. B481 (2000) 97-106

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, LaTeX, no figures, arguments on the action and symmetry are improved

Scientific paper

10.1016/S0370-2693(00)00418-4

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.

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