Noncommutative Perturbative Dynamics

Noncommutative Perturbative Dynamics

Dec. 1999 | Shiraz Minwalla, Mark Van Raamsdonk, Nathan Seiberg
This paper studies the perturbative dynamics of noncommutative field theories on R^d, revealing an intriguing mixing of UV and IR phenomena. High-energy virtual particles in loops produce non-analyticity at low momentum, leading to singularities in the low-energy effective action even when the original theory is massive. Nonplanar diagrams, though divergent, are interpreted as IR divergences. The UV/IR mixing arises from noncommutativity, reminiscent of channel duality in open string theory. The paper analyzes scalar field theories, showing that nonplanar one-loop diagrams in φ³ in six dimensions and φ⁴ in four dimensions are UV finite but exhibit IR singularities. These singularities are similar to closed string poles in open string theory. Higher-order diagrams are explored, with nonplanar graphs showing convergence due to damping effects of rapid oscillations. The paper discusses the stringy nature of noncommutative theories, noting that maximal noncommutativity leads to stringy behavior. The effective action is analyzed, showing that noncommutative theories can exhibit IR singularities even when massive. The paper concludes that UV/IR mixing is a key feature of noncommutative field theories, with implications for renormalization and the behavior of correlation functions.This paper studies the perturbative dynamics of noncommutative field theories on R^d, revealing an intriguing mixing of UV and IR phenomena. High-energy virtual particles in loops produce non-analyticity at low momentum, leading to singularities in the low-energy effective action even when the original theory is massive. Nonplanar diagrams, though divergent, are interpreted as IR divergences. The UV/IR mixing arises from noncommutativity, reminiscent of channel duality in open string theory. The paper analyzes scalar field theories, showing that nonplanar one-loop diagrams in φ³ in six dimensions and φ⁴ in four dimensions are UV finite but exhibit IR singularities. These singularities are similar to closed string poles in open string theory. Higher-order diagrams are explored, with nonplanar graphs showing convergence due to damping effects of rapid oscillations. The paper discusses the stringy nature of noncommutative theories, noting that maximal noncommutativity leads to stringy behavior. The effective action is analyzed, showing that noncommutative theories can exhibit IR singularities even when massive. The paper concludes that UV/IR mixing is a key feature of noncommutative field theories, with implications for renormalization and the behavior of correlation functions.
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Understanding Noncommutative perturbative dynamics