Moments of the 2D SHE at criticality

We study the stochastic heat equation in two spatial dimensions with a multiplicative white noise, as limit of driven by noise that is mollified space and time. As mollification radius $ \varepsilon\to 0 $, we tune coupling constant near critical point, show single time correlation functions converge to written terms an explicit non-trivial semigroup. Our approach consists steps. First convergence resolvent (tuned) two-dimensional delta Bose gas, adapting framework Dimock Rajeev (2004) our setup mollification. Then match this Laplace transform