Infinite divisibility conjecture for logarithmic GMC total mass

Let $M_\mu$ be a Gaussian multiplicative chaos measure on $\mathcal{D}$ and let $\varphi$ be a test function. Define the weighted total mass

$$\int_{\mathcal{D}}\varphi(x)\,M_\mu(dx).$$

Infinite divisibility conjecture. The distribution of

$$\log\int_{\mathcal{D}}\varphi(x)\,M_\mu(dx)$$

is infinitely divisible. Infinite divisibility is known for the Selberg and Morris integral probability distributions, but the general GMC assertion is left as a conjecture in the supplied source.