Exact solution of matricial $\Phi^3_2$ 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-$\mathcal{N}$ limit to integral equations that we solve exactly for all correlation functions. Remarkably, these functions are analytic in the $\Phi^3$ coupling constant, although bounds on individual graphs justify only Borel summability.   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. 
Harald Grosse (Vienna), Akifumi Sako (Tokyo) and Raimar Wulkenhaar   (M\"unster)
math-ph hep-th math.MP