∗Trek II: ∗ _{n} operations, open Wilson lines and the SeibergWitten map
Abstract
Generalizations of the ∗product (e.g., nary ∗ _{n} operations) appear in various places in the discussion of noncommutative gauge theories. These include the oneloop effective action of noncommutative gauge theories, the couplings between massless closed and open string modes, and the SeibergWitten map between the ordinary and noncommutative YangMills 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 oneloop 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 SeibergWitten map in the U(1) case.
 Publication:

Nuclear Physics B
 Pub Date:
 October 2001
 DOI:
 10.1016/S05503213(01)004023
 arXiv:
 arXiv:hepth/0011125
 Bibcode:
 2001NuPhB.614..305L
 Keywords:

 High Energy Physics  Theory
 EPrint:
 30 pages, AMSLaTeX using JHEP.cls., clarifications made, misprints corrected, references added