Large-Charge Limit of AdS Boson Stars with Mixed Boundary Conditions

TL;DR

This paper constructs charged AdS boson star solutions with mixed boundary conditions, analyzing how the mass-charge ratio depends on boundary conditions and providing a numerical and analytical characterization of this dependence.

Contribution

It introduces a class of charged AdS boson star solutions with mixed boundary conditions and characterizes the boundary condition dependence of their mass-charge ratio.

Findings

The mass-charge ratio coefficient increases monotonically with boundary condition parameter k.

For small k, the coefficient grows linearly with k.

As k approaches infinity, the coefficient approaches a maximum at a rate proportional to k^{-3/2}.

Abstract

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.