Stochastic Quantisation of the fractional Φ4 model in the full subcritical regime

Abstract: We prove the existence of the fractional Φ4 Euclidean quantum field theory on ℝ3 in the full subcritical regime via parabolic stochastic quantisation. Our approach is based on the use of a novel truncated flow equation for the effective description of the model at sufficiently small scales and on coercive estimates for the non-linear stochastic partial differential equation describing the interacting field.