2d Sinh-Gordon model on the infinite cylinder

The 2d (massless) Sinh-Gordon model is amongst the simplest 2d quantum field theories that are expected to be integrable (= infinitely many symmetries), but without conformal symmetry. In this talk I will explain a rigorous construction of this model and its vertex correlations (= Laplace transforms) on the infinite cylinder using probability theory. A fundamental role is played by the Sinh-Gordon Hamiltonian and I will explain how the theory of Gaussian multiplicative chaos can be used to analyze this linear map. This talk will be based on joint work with Colin Guillarmou and Vincent Vargas.