Stochastic quantization associated with the $$\exp (\Phi )_2$$-quantum field model driven by space-time white noise on the torus in the full $$L^1$$-regime

Abstract

AbstractThe present paper is a continuation of our previous work (Hoshino et al., J Evol Equ 21:339–375, 2021) on the stochastic quantization of the $$\exp (\Phi )_2$$ exp ( Φ ) 2 -quantum field model on the two-dimensional torus. Making use of key properties of Gaussian multiplicative chaos and refining the method for singular SPDEs introduced in the previous work, we construct a unique time-global solution to the corresponding parabolic stochastic quantization equation in the full “$$L^{1}$$ L 1 -regime” $$\vert \alpha \vert <\sqrt{8\pi }$$ | α | < 8 π of the charge parameter $$\alpha $$ α . We also identify the solution with an infinite-dimensional diffusion process constructed by the Dirichlet form approach.