Noncommutative Perturbative Dynamics

Noncommutative Perturbative Dynamics

Dec. 1999 | Shiraz Minwalla, Mark Van Raamsdonk1, Nathan Seiberg2
The paper studies the perturbative dynamics of noncommutative field theories on \(\mathcal{R}^d\), focusing on scalar field theories. It finds an intriguing mixing of UV and IR effects, where 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. The paper discusses the UV/IR mixing arising from the underlying noncommutativity and compares it to the channel duality of the double twist diagram in open string theory. It also explores higher-order Feynman diagrams and their properties, including the limit of maximal noncommutativity, where the theory is dominated by planar graphs and exhibits stringy behavior. The authors interpret some divergences as IR divergences and propose a procedure to deal with them without introducing counterterms. The paper concludes with an investigation into the properties of noncommutative gauge theories and an appendix presenting the expression for the Feynman integral of an arbitrary noncommutative diagram in terms of Schwinger parameters.The paper studies the perturbative dynamics of noncommutative field theories on \(\mathcal{R}^d\), focusing on scalar field theories. It finds an intriguing mixing of UV and IR effects, where 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. The paper discusses the UV/IR mixing arising from the underlying noncommutativity and compares it to the channel duality of the double twist diagram in open string theory. It also explores higher-order Feynman diagrams and their properties, including the limit of maximal noncommutativity, where the theory is dominated by planar graphs and exhibits stringy behavior. The authors interpret some divergences as IR divergences and propose a procedure to deal with them without introducing counterterms. The paper concludes with an investigation into the properties of noncommutative gauge theories and an appendix presenting the expression for the Feynman integral of an arbitrary noncommutative diagram in terms of Schwinger parameters.
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