The Φ43 measure is one of the easiest non-trivial examples of a Euclidean quantum field theory (EQFT) whose rigorous construction in the 1970’s has been one of the celebrated achievements of the Constructive QFT community. In recent years, progress in the field of singular stochastic PDEs, initiated by the theory of regularity structures, has allowed for a new construction of the Φ43 EQFT as the invariant measure of a previously ill-posed Langevin dynamics—a strategy originally proposed by Parisi and Wu (’81) under the name Stochastic Quantisation. In this talk, I will demonstrate that the same idea also allows to transfer the large deviation principle for the Φ43 dynamics, obtained by Hairer and Weber (’15), to the corresponding EQFT. Our strategy is inspired by earlier works of Sowers (’92) and Cerrai and Röckner (’05) for non-singular dynamics and potentially also applies to other EQFT measures. This is joint work with Avi Mayorcas (University of Bath), see arXiv:2402.00975. If time permits, I will briefly explain how similar techniques may be used to study exit problems for the 3D Stochastic Allen–Cahn equation which is a joint work in progress with Ioannis Gasteratos (TU Berlin).
