Open Wilson lines as closed strings in non-commutative field theories

Abstract

Open Wilson line operators and the generalized star product have been studied extensively in non-commutative gauge theories. We show that they also show up in non-commutative scalar field theories as universal structures. We first point out that the dipole picture of non-commutative geometry provides an intuitive argument, for robustness of the open Wilson lines and generalized star products therein. We calculate the one-loop effective action of the non-commutative scalar field theory with cubic self-interaction and show explicitly that the generalized star products arise in the non-planar part. It is shown that, in the low-energy, large non-commutativity limit, the non-planar part is expressible solely in terms of the scalar open Wilson line operator and descendants, the latter being interpreted as composite operators representing a closed string.