If $\Sigma$ is a Riemann surface, there are two measures on $\text{H}^s(\Sigma)$:
 1. the *Gaussian free field* $h(z)$ and
 2. the *Gaussian multiplicative chaos* $\mu(z)= \lim_{\epsilon\to0} e^{\gamma h_\epsilon(z)}\epsilon^{\gamma^2/2}$.

See for instance Theorem 2.1 of [Berestycki's notes][1]. 

My **question** is: what is the relation between 1 and 2? For instance, is there a way of making a formula a bit like $\frac{d}{d\gamma}\mu(z)\vert_{\gamma=0}=h(z)$ precise?


  [1]: https://www.math.stonybrook.edu/~bishop/classes/math638.F20/Berestycki_GFF_LQG.pdf