A Solvable Four-Dimensional QFT

Abstract

We review a sequence of papers in which we show that the quartic matrix model with an external matrix is exactly solvable in terms of the solution of a non-linear integral equation. The interacting scalar model on four-dimensional Moyal space is of this type, and our solution leads to the construction of Schwinger functions. Taking a special limit leads to a QFT on \(\mathbb{R}^{4}\) which satisfies growth property, covariance and symmetry. There is numerical evidence for reflection positivity of the 2-point function for a certain range of the coupling constant.