  The goal of this article is to expand on the relationship between random
matrix and multiplicative chaos theories using the integrability properties of
the circular beta-ensembles. We give a comprehensive proof of the
multiplicative chaos convergence for the characteristic polynomial and
eigenvalue counting function of the circular beta-ensembles throughout the
subcritical phase, including negative powers. This generalizes recent results
in the unitary case, [NSW20,BF22], to any beta>0 and for the eigenvalue
counting field.
