A nontrivial solvable noncommutative φ^3 model in 4 dimensions

Details A nontrivial solvable noncommutative φ^3 model in 4 dimensions A nontrivial solvable noncommutative φ^3 model in 4 dimensions

2006-03-07

arxiv.org/abs/hep-th/0603052v2

JHEP0608:008,2006

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, 2 figures. V2: typos fixed

Scientific paper

10.1088/1126-6708/2006/08/008

We study the quantization of the noncommutative selfdual \phi^3 model in 4 dimensions, by mapping it to a Kontsevich model. The model is shown to be renormalizable, provided one additional counterterm is included compared to the 2-dimensional case which can be interpreted as divergent shift of the field \phi. The known results for the Kontsevich model allow to obtain the genus expansion of the free energy and of any n-point function, which is finite for each genus after renormalization. No coupling constant or wavefunction renormalization is required. A critical coupling is determined, beyond which the model is unstable. This provides a nontrivial interacting NC field theory in 4 dimensions.

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