Interacting Open Wilson Lines from Noncommutative Field Theories 1

In noncommutative field theories, it was known that one-loop effective action describes propagation of non-interacting open Wilson lines, obeying the flying dipole’s relation. We show that two-loop effective action describes cubic interaction among ‘closed string’ states created by open Wilson line operators. Taking d-dimensional λ[Φ]⋆-theory as the simplest setup, we compute nonplanar contribution at low-energy and large noncommutativity limit. We find that the contribution is expressible in a remarkably simple cubic interaction involving scalar open Wilson lines only and nothing else. We show that the interaction is purely geometrical and noncommutative in nature, depending only on sizes of each open Wilson line. 1 Work supported in part by the BK-21 Initiative in Physics, the KRF International Collaboration Grant, the KRF Grant 2001-015-DP0082, the KOSEF Interdisciplinary Research Grant 98-07-02-07-01-5, the KOSEF Leading Scientist Program, and the KOSEF Brain-Pool Program.