Stochastic quantization associated with the $$\exp (\Phi )_2$$ exp ( Φ ) 2 -quantum field model driven by space-time white noise on the torus

We consider a quantum field model with exponential interactions on the two-dimensional torus, which is called the $$\exp (\Phi )_{2}$$ -quantum field model or Høegh-Krohn’s model. In the present paper, we study the stochastic quantization of this model by singular stochastic partial differential equations, which is recently developed. By the method, we construct a unique time-global solution and the invariant probability measure of the corresponding stochastic quantization equation and identify it with an infinite-dimensional diffusion process, which has been constructed by the Dirichlet form approach.