Exact solution of matricial ${\Phi }_2^3$ quantum field theory

We apply a recently developed method to exactly solve the ${\Phi }^3$ matrix model with covariance of a two-dimensional theory, also known as regularised Kontsevich model. Its correlation functions collectively describe graphs on a multi-punctured 2-sphere. We show how Ward–Takahashi identities and Schwinger–Dyson equations lead in a special large-$N$ limit to integral equations that we solve exactly for all correlation functions. The solved model arises from noncommutative field theory in a special limit of strong deformation parameter. The limit defines ordinary 2D Schwinger functions which, however, do not satisfy reflection positivity.