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. In particular, I will explain how the theory of Gaussian multiplicative chaos can be used to analyze the spectrum of the corresponding Sinh-Gordon Hamiltonian. This talk will be based on joint work with Colin Guillarmou and Vincent Vargas.