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

Understand

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.