  It was recently shown that charged AdS boson stars can reproduce the
universal structure of the lowest scaling dimension in the subsector of a CFT
with fixed large global $U(1)$ charge $Q$. Using the model consisting of
Einstein-Maxwell gravity with a negative cosmological constant, coupled to a
$U(1)$-charged conformally massless scalar with the fourth-order self
interaction, we construct a class of charged AdS boson star solutions in the
large $Q$ limit, where the scalar field obeys a mixed boundary condition,
parameterized by $k$ that interpolates between the Neumann and Dirichlet
boundary conditions corresponding to $k=0$ and $\infty$ respectively. By
varying $k$, we numerically read off the $k$ dependence of the leading
coefficient $c_{3/2}(k) \equiv \lim_{Q\rightarrow \infty} M/Q^{3/2}$. We find
that $c_{3/2}(k)$ is a monotonously increasing function which grows linearly
when $k$ is sufficiently small. When $k\rightarrow \infty$, $c_{3/2}(k)$
approaches the maximal value at a decreasing rate given by $k^{-3/2}$ . We also
obtain a close form expression that fits the numerical data for the entire
range of $k$ within $10^{-4}$ accuracy.
