The 2d Sinh and Sine Gordon models are interacting quantum field theories that are expected to have additional structure - they are "integrable". A concrete manifestation of this is that many physically relevant quantities are expected to have exact formulas. In this talk I will discuss the rigorous probabilistic construction of these models and their vertex correlations on the infinite cylinder. The construction is based on the analysis of the ground states of the corresponding quantum operators, enabled by the theory of Gaussian multiplicative chaos. If time permits, I shall also discuss the scaling of the smallest eigenvalues as the cylinder width goes to infinity. This is based on joint works with Colin Guillarmou, Remi Rhodes, and Vincent Vargas.
Zoom link: https://icts-res-in.zoom.us/j/96401100280?pwd=NVVpR05BcmprMDVJK2oydGxudlE0UT09
Meeting ID: 964 0110 0280