*-Trek II: *_n Operations, Open Wilson Lines and the Seiberg-Witten Map

Details *-Trek II: *_n Operations, Open Wilson Lines and the Seiberg-Witten Map *-Trek II: *_n Operations, Open Wilson Lines and the Seiberg-Witten Map

2000-11-14

arxiv.org/abs/hep-th/0011125v3

Nucl.Phys. B614 (2001) 305-329

Physics

High Energy Physics

High Energy Physics - Theory

30 pages, AMSLaTeX using JHEP.cls., clarifications made, misprints corrected, references added

Scientific paper

10.1016/S0550-3213(01)00402-3

Generalizations of the *-product (e.g. n-ary *_n operations) appear in various places in the discussion of noncommutative gauge theories. These include the one-loop effective action of noncommutative gauge theories, the couplings between massless closed and open string modes, and the Seiberg-Witten map between the ordinary and noncommutative Yang-Mills fields. We propose that the natural way to understand the *_n operations is through the expansion of an open Wilson line. We establish the connection between an open Wilson line and the *_n operations and use it to: (I) write down a gauge invariant effective action for the one-loop F^4 terms in the noncommutative N=4 SYM theory; (II) find the gauge invariant couplings between the noncommutative SYM modes and the massless closed string modes in flat space; (III) propose a closed form for the Seiberg-Witten map in the U(1) case.

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