We consider the scalar φ4 model on the 4-dimensional noncommutative Moyal space. This is the critical dimension where the model becomes just-renormalisable. At the self-dual point, this model breaks down to a matrix model, where the noncommutativity of the underlying space is related to the size N of the matrix. Assuming a formal expansion in 1/N, the Dyson-Schwinger equations (after applying Ward identities) decouple which leads to (non-)linear integral equations at each order in 1/N. We will present and discuss from different perspectives the leading order (genus g = 0) result of the 2-point function, which is a resummation of infinitely many Feynman diagrams. We will also discussion the Hopf-algebraic renormalision of this model in the sense of Connes-Kreimer, which has the same complexitiy as an ordinary just-renormalisable QFT.
This video was produced by the University of Münster, as part of the workshop Stochastic Analysis meets QFT – critical theory.
