Noncommutative perturbative dynamics. (English) Zbl 0959.81108

Summary: We study the perturbative dynamics of noncommutative field theories on \(\mathbb{R}^d\), and find an intriguing mixing of the UV and the IR. High energies of virtual particles in loops produce non-analyticity at low momentum. Consequently, the low energy effective action is singular at zero momentum even when the original noncommutative field theory is massive. Some of the nonplanar diagrams of these theories are divergent, but we interpret these divergences as IR divergences and deal with them accordingly. We explain how this UV/IR mixing arises from the underlying noncommutativity. This phenomenon is reminiscent of the channel duality of the double twist diagram in open string theory.


81T75 Noncommutative geometry methods in quantum field theory
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
58B32 Geometry of quantum groups
Full Text: DOI arXiv