JHEP 04, 220 (2021)

Large-charge limit of AdS boson stars with mixed boundary conditions

Shi-Fa Guo, Hai-Shan Liu, H. Lü and Yi Pang*

Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin, 300350, China

* pangyi1@tju.edu.cn

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 ∞ respectively. By varying k, we numerically read off the k dependence of the leading coefficient c_3/2(k) ≡ lim_Q→∞ 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 → ∞, 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.