Progress in solving a noncommutative quantum field theory in four dimensions

Understand

We study the noncommutative \phi^4_4-quantum field theory at the self-duality point.

• This model is renormalisable to all orders as shown in earlier work of us and does not have a Landau ghost problem.
• Using the Ward identity of Disertori, Gurau, Magnen and Rivasseau, we obtain from the Schwinger-Dyson equation a non-linear integral equation for the renormalised two-point function alone.
• The non-trivial renormalised four-point function fulfils a linear integral equation with the inhomogeneity determined by the two-point function.