Parity Symmetry Breaking and Kink Hairy Black Hole

Abstract

Motivated by the Kibble-Zurek mechanism and the Gubser's argument for the charged scalar hairs near the black hole horizon in a spacetime with negative cosmological constant, we realize the kink hairs in a planar Schwarzschild-AdS black hole. By increasing the chemical potential across the critical point of the dual boundary field theory, the former $Z_2$ symmetry of the real scalar fields spontaneously break and form kinks in the bulk. Correspondingly, in the AdS boundary it resembles the kinks in a one-dimensional chain. The relation between the kink numbers and the quench rate obeys a universal scaling law which satisfies the Kibble-Zurek's prediction.Comment: 10 pages; 3 figure