Renormalisation of \phi^4-theory on noncommutative R^4 to all orders

TL;DR

This paper proves that a specific noncommutative -dimensional  -model is renormalisable at all orders, using matrix model reformulation, orthogonal polynomials, and flow equations for ribbon graphs.

Contribution

It introduces a comprehensive proof of all-order renormalisability for the duality-covariant noncommutative --model, combining multiple advanced techniques.

Findings

The model is renormalisable to all orders.

Reformulation as a dynamical matrix model facilitates analysis.

Flow equations and power-counting theorems support renormalisation.

Abstract

We present the main ideas and techniques of the proof that the duality-covariant four-dimensional noncommutative \phi^4-model is renormalisable to all orders. This includes the reformulation as a dynamical matrix model, the solution of the free theory by orthogonal polynomials as well as the renormalisation by flow equations involving power-counting theorems for ribbon graphs drawn on Riemann surfaces.