Interacting Open Wilson Lines in Noncommutative Field Theories
arXiv:hep-th/0110215 · doi:10.1103/PhysRevD.65.046003
Abstract
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 lines. Taking d-dimensional noncommutative [Φ^3] 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.
v1: 27 pages, Latex, 7 .eps figures v2: minor wording change + reference added
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- Nonplanar Anomalies in Noncommutative Theories and the Green-Schwarz Mechanism
- Open Wilson Lines and Group Theory of Noncommutative Yang-Mills Theory in Two Dimensions
- On the UV renormalizability of noncommutative field theories
- Open Wilson Lines as States of Closed String
- From UV/IR mixing to closed strings
- Anatomy of Two-Loop Effective Action in Noncommutative Field Theories
- Interacting Dipoles from Matrix Formulation of Noncommutative Gauge Theories
- Gauge Invariance and Noncommutativity
- UV-IR mixing and the quantum consistency of noncommutative gauge theories
- Bound-state gravity from higher derivatives
- Strings, Dipoles and Fuzzy Spheres
- Softer Hard Scattering and Noncommutative Gauge-String Duality
- One-loop unitarity of string theories in a constant external background and their Seiberg-Witten limit