Moyal Representation of the String Field Star Product in the Presence of a B-background
arXiv:hep-th/0211199 · doi:10.1103/PhysRevD.67.126003
Abstract
In this paper we show that in the presence of an anti-symmetric tensor -background, Witten's star algebra for open string fields persists to possess the structure of a direct product of commuting Moyal pairs. The interplay between the noncommutativity due to three-string overlap and that due to the -background is our main concern. In each pair of noncommutative directions parallel to the -background, the Moyal pairs mix string modes in the two directions and are labeled, in addition to a continuous parameter, by {\it two} discrete values as well. However, the Moyal parameters are -dependent only for discrete pairs. We have also demonstrated the large- contraction of the star algebra, with one of the discrete Moyal pairs dropping out while the other giving rise to the center-of-mass noncommutative function algebra.
minor notation change
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