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

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 $c_{3/2}(k)\equiv {\lim }_{Q\to \infty }M/Q^{3/2}$. We find that $c_{3/2}(k)$ is a monotonously increasing function which grows linearly when $k$ is sufficiently small. When $k\to \infty$, $c_{3/2}(k)$ 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.

Latex, 17 pages, 7 figures, refs added, to appear in JHEP

References in corpus (5)

• Feynman diagrams and the large charge expansion in $3-\epsilon$ dimensions
• Hairy black holes and the endpoint of AdS${}_4$ charged superradiance
• Matrix models at large charge
• Superfluid and Metamagnetic Phase Transitions in $\omega$-deformed Gauged Supergravity
• The large charge expansion and AdS/CFT

Cited by in corpus (3)

• Improved Reall-Santos method for AdS black holes in general 4-derivative gravities
• Hairy black holes in AdS with Robin boundary conditions
• $\ell$-Boson stars in anti-de Sitter spacetime