Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-04-05
JHEP0503:042,2005
Physics
High Energy Physics
High Energy Physics - Theory
40 pages, 5 figures. Version to be submitted to JHEP. Some interesting and previouusly unpublished results are included here.
Scientific paper
10.1088/1126-6708/2005/03/042
In this paper we study the midpoint structure of the algebra of open strings from the standpoint of the operator/Moyal formalism. We construct a split string description for the continuous Moyal product of hep-th/0202087, study the breakdown of associativity in the star algebra, and identify in infinite sequence of new (anti)commutative coordinates for the star product in in the complex plane. We also explain how poles in the open string non(anti)commutativity parameter correspond to certain ``null'' operators which annihilate the vertex, implying that states proportional to such operators tend to have vanishing star product with other string fields. The existence of such poles, we argue, presents an obstruction to realizing a well-defined formulation of the theory in terms of a Moyal product. We also comment on the interesting, but singular, representation $L_0$ which has appeared prominently in the recent studies of Bars {\it et al}.
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