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

Tsunehide Kuroki
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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.

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Tsunehide Kuroki. 2000-01-14. Noncommutativities of D-branes and $θ$-changing Degrees of Freedom in D-brane Matrix Models. https://doi.org/10.1016/s0370-2693(00)00418-4

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